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Ratio: The ratio of two quantities a and b in the same units is the fraction a/b and we write it as a : b.
- In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.
- Example: The ratio 5 : 9 represents 5/9 With antecedent = 5, consequent = 9.
[Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.]
Example: 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.
Proportion: The equality of two ratios is called proportion.
- If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.
- Here a and d are called extremes, while b and c are called mean terms.
- Product of means = Product of extremes.
- Thus, a : b :: c : d (b x c) = (a x d).
Fourth Proportional: If a : b = c : d, then d is called the fourth proportional to a, b, c.
Third Proportional: a : b = c : d, then c is called the third proportion to a and b.
Mean Proportional: Mean proportional between a and b is ab.
Comparison of Ratios: We say that (a : b) > (c : d) <=> a / b > c / d
Compounded Ratio: The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).
Duplicate Ratios: Duplicate ratio of (a : b) is (a2 : b2).
- Sub-duplicate ratio of (a : b) is (a1/2 : b1/2).
- Triplicate ratio of (a : b) is (a3 : b3).
- Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).
- If a/b = c/d, then a + b / a – b =c + d / c – d [Componendo and dividendo]
Variations
- We say that x is directly proportional to y, if x = ky for some constant k and we write, x ∝ y.
- We say that x is inversely proportional to y, if xy = k for some constant k and we write, x ∝ 1/ y
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Ratio and proportion – Question and Answers
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Question 1If the area of two circles are in the ratio 169:196 then the ratio of their radii is?10:11
11:1212:1313:14 Question 1 Explanation: If r and R are radii if two circles, then
pi * r^2 /pi * R^2 = 169 / 196
r^2 / R^2 = 169 / 196 = (13/14)^2
so r/R = 13/14Question 2The salaries of A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?3 : 3 : 1010 : 11 : 2023 : 33 : 60Cannot be determinedQuestion 2 Explanation: Let A = 2k, B = 3k and C = 5k
A’s new salary = (115 / 100) of 2k = (115 / 100) x 2k = 23k / 10
B’s new salary = (110 / 100) of 3k = (110 / 100) x 3k = 33k / 10
C’s new salary = (120 / 100) of 5k = (120 / 100) x 5k = 6k
New ratio = [23k / 10 : 33k / 10 : 6k]
= 23 : 33 : 60
Question 3If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?2:53:75:37:3Question 3 Explanation: Let 40% of A = 2 / 3 B
Then, 40A / 100 = 2B / 3
2A / 5 = 2B / 3
A / B = (2 / 3 * 5 / 2) = 5 / 3
A : B = 5 : 3
Question 4The fourth proportional to 5, 8, 15 is?18241920Question 4 Explanation: Let the fourth proportional to 5, 8, 15 be x
Then, 5 : 8 : 15 : x
5x = (8 x 15)
x = (8 x 15) / 5 = 24
Question 5Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is?27334955Question 5 Explanation: Let the numbers be 3x and 5x
Then, 3x – 9 / 5x – 9 = 12 / 23
23 (3x – 9) = 12 (5x – 9)
9x = 99
x = 11
The smaller number = (3 x 11) = 33
Question 6In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?50100150200Question 6 Explanation: Then, sum of their values = Rs. {(25x / 100) +[(10 * 2x) / 100)]+ (5 * 3x /100)} = Rs. 60x / 100
(60x / 100) = 30
x = (30 x 100) / 60 = 50
Hence, the number of 5 p coins = (3 x 50) = 150
Question 7The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?8:917:1821:22Cannot be determinedQuestion 7 Explanation: Originally, let the number of boys and girls in the college be 7x and 8x respectively
Their increased number is (120% of 7x) and (110% of 8x)
(120 / 100 * 7x) And (110 / 100 * 8x)
42x / 5 and 44x / 5
The required ratio = 42x / 5 : 44x / 5 = 21 : 22
Question 8Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit’s salary?17,00020,00025,50038000Question 8 Explanation: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively
Then, (2x + 4000) / (3x + 4000) = 40 / 57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit’s present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000
Question 9If 0.75 : x :: 5 : 8, then x is equal to?1.121.201.251.30Question 9 Explanation: (x * 5) = (0.75 * 8) x = 6 / 5 = 1.20Question 10The sum of three numbers is 98. If the ratio of the first to second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is?20304858Question 10 Explanation: Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 = (5 x 3 / 5 : 8 x 3 / 5) = 3 : (24 / 5)
A : B : C = 2 : 3 : (24 / 5) = 10 : 15 : 24
B = 98 x (15 / 49) = 30
Question 11A and B together have Rs. 1210. If 4/15 of A’s amount is equal to 2/5 of B’s amount, how much amount does B have?460484550664Question 11 Explanation: 4 /15A = 2 /5B
A = (2/5 * 15/4)B
A = 3 / 2B
A / B = 3 / 2
A : B = 3 : 2
B’s share = Rs. (1210 * (2 / 5)) = Rs. 484
Question 12Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is?2 : 53 : 54 : 56 : 7Question 12 Explanation: Let the third number be x
Then the first number = 120% of x = 120x / 100 = 6x /5
Second number = 150% of x = 150x / 100 = 3x /2
Ratio of first two numbers = 6x / 5 : 3x / 2 = 12x : 15x = 4 : 5
Question 13A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?50015002000None of theseQuestion 13 Explanation: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively
Then, 4x – 3x = 1000
x = 1000
B’s share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000
Question 14Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?2 : 3: 46 : 7 : 86 : 8 : 9None of theseQuestion 14 Explanation: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)
= (140/100 * 5x) ,(150/100 * 7x) and (175/100 * 8x)
= 7x, 21x /2 and 14x
The required ratio = 7x : 21x /2 : 14x
= 14x : 21x : 28x
= 2 : 3 : 4
Question 15In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2,
then the quantity of water to be further added is?20304060Question 15 Explanation: Quantity of milk = (60 * 2/3)litres = 40 litres
Quantity of water in it = (60 – 40) litres = 20 litres
New ratio = 1 : 2
Let quantity of water to be added further be x litres
Then, milk : water = (40 / 20 + x )
Now, (40 / (20 + x)) = 1 / 2
20 + x = 80
x = 60
Quantity of water to be added = 60 litresQuestion 16A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs.2.40 the number of girls is?35404550Question 16 Explanation: Let x be the number of boys and y be the number of girls
Given total number of boys and girls = 100
x + y = 100
A boy gets Rs. 3.60 and a girl gets Rs. 2.40
The amount given to 100 boys and girls = Rs. 312
3.6x + 2.4y = 312
By Solving
3.6x + 3.6y = 360 multiplying by 3.6
3.6x + 2.4y1.20yy = 312 = 48 = 40
The number of girls is 40
Question 17In a mixture 60 litres, the ratio of milk and water 2:1. If the this ratio is to be 1:2, then the quantity of water to be further added is?20304060Question 17 Explanation: Quantity of milk = 60 × 23 = 40 litres
Quantity of water in it = (60 − 40) litres = 20 litres
New ratio = 1 : 2
Let, the quantity of water to be added further be x litres
Then milk : water = 4020 + x
Now, 4020 + x20 + x ⇒x =12 = 80 = 60
Question 18Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is?2 : 5
3 : 54 : 55 : 4Question 18 Explanation: Let the third number be x
Then, first number = 120% of x = 120 x 100=6 x 5
Second number = 150% of x = 150 x 100 = 3 x 2
Ratio of first two numbers = 6 x 5 : 3 x 2 = 4 : 5
Question 19A sum of Rs. 36.90 is made up of 180 coins which are either 10 paise coins or 25 p coins. The number of 10 p coins is?48545660Question 19 Explanation: Total number of coins = 180
Let x be number of 10p coins and y be number of 25p coins
x + y = 180 ——–(i)
Step (ii) Given 10p coins and 25p coins make the sum = Rs. 36.90
10x 100 + 25y 100 ⇒ 10x + 25y = 36.9 = 3690—–(ii)
Step (iii)
Solving (i) and (ii),
10x + 10y10x + 25y − 15yy = 1800 = 3690 = 1890 = 126
Substitute y value in equation (i)
x = 180 – 126 = 54
Number of 10p coins = 54
Question 20The salaries A, B, C are in the ratio 2:3:5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?3 : 3 : 1010 : 11 : 2023 : 33 : 60Cannot be determinedQuestion 20 Explanation: Let A = 2k, B = 3k and C = 5k
A’s new salary = (115100 × 2k) = 23k10
B’s new salary = (110100 × 3k) = 33k10
C’s new salary = (120100 × 5k) = 6k
⇒New ratio = (23k10 : 33k10 : 6k) = 23 : 33 : 60
Question 21Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit’s salary?Rs. 17,000Rs. 20,000Rs. 34,000Rs. 38,000Question 21 Explanation: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively
then, 2x + 40003x + 4000 ⇒57 × (2x + 4000) 6x3x = 4057 = 40 × (3x + 4000) = 68,000 = 34,000
Sumit’s present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000
Question 22The sum of three numbers is 98. If the ratio of the first to second is 2:3 and that of the second to the third is 5:8, then the second number is?20
304858Question 22 Explanation: Let the three parts be A, B, C. Then,
A:B=2:3 and B:C=5:8
=> 5 × 35 : 8 × 35 ⇒ A : B : C = 2 : 3 : 245 = 10 : 15 : 24
=> B = 98 × 1549 = 30 = 3 : 245
Question 23Rs.432 is divided amongst three workers A, B and C such that 8 times A’s share is equal to 12 times B’s share which is equal to 6 times C’s share. How much did A get?Rs.192
Rs. 133Rs. 144Rs. 128Question 23 Explanation: 8 times A’s share = 12 times B’s share = 6 times C’s share
Note that this is not the same as the ratio of their wages being 8 : 12 : 6
In this case, find out the L.C.M of 8, 12 and 6 and divide the L.C.M by each of the above numbers
to get the ratio of their respective shares
The L.C.M of 8, 12 and 6 is 24
Therefore, the ratio A : B : C is
248 : 2412 : 246 ⇒ A : B : C :: 3 : 2 : 4
The sum of the total wages =3x + 2x + 4x = 432
9x = 432 or x = 48
Hence A gets 3 × 48 = Rs 144
Question 24If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days?120 men
122 men128 men134 menQuestion 24 Explanation: Amount of work done by 20 men = 24 women = 40 boys or 1 man = 1.2 woman = 2 boys
Let us therefore, find out the amount of men required
If only men were working on the job, to complete the new job under the new conditions and then make adjustments for the women and children working with the men
The man hours required to complete the new job = 4 times the man hours required to complete the old job
(As the new job is 4 times as big as the old job)
Let n be the number of men required
n × 5 × 12 = 20 × 8 × 12 × 4 = or n = 128
i.e. 128 men working on the job will be able to complete the given job
However, the problem states that 6 women and 2 boys are working on the job
6 women $ = \dfrac{6}{1.2} = 5 men and 2 boys = 1 man
∴ The equivalent of 5 + 1 = 6 men are already working
Thus, final number of men working
= 128 − 6 = 122 men
Question 25P,Q and R enter into a partnership with capitals in the ratio 3:2:1. After 4 months, P leaves the business and after 4 more months Q also leaves the business and R continues till the end of the year. If R takes 10 of the profit for managing the business, then what part of the profit does R get?37%
36%27%30%Question 25 Explanation: Let Rs 100 be the profit
Rs 90 is to be divided in the ratio 12 : 16 : 12. i.e 3 : 4 : 3
R gets 310 × 90 = 27 and 10 for managing
Thus 27 + 10 = 37%
Question 26An outgoing batch of students wants to gift a PA system worth Rs 4,200 to their school. If the teachers, offer to pay 50% more than the students and an external benefactor gives three times the teacher’s contribution, then how much should the teachers donate?Rs 600
Rs 840Rs 900Rs 1,200Question 26 Explanation: The ratio of the share students : teacher : benefactor = 1 : 1.5 : 4.5
So the proportion to teacher’s share = 1.57
Hence, the teachers would donate 1.57 × 4200 = Rs 900
Question 27IBM and KTC quote for a tender. On the tender opening day, IBM realizes that their quotations are in the ratio 7:4 and hence decreases its price during negotiations to make it Rs 1 Lakh lower than KTC’s quoted price. KTC realizes that the final quotes of the two were in the ratio 3:4. What was the price at which IBM won the bid?Rs 7 LakhRs 4 LakhRs 3 LakhRs 1.5 LakhQuestion 27 Explanation: IBM initially quoted Rs 7x lakh. KTC quoted 4x lakh
IBM’s final quote = (4×1) Lakh
Thus, 4x − 14x ⇒ x = 34 = 1
IBM’s bid winning price = Rs 3. Lakh
So IBM wins the bid at 4×1= Rs. 3 lakh
Question 28The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is?2 : 1
5 : 199 : 61227 : 133Question 28 Explanation: Proportion of milk in 3 samples is 23,35,58
Proportion of water in 3 samples is 13,25,38
Since equal quantities are taken,
Total proportion of milk is 23 + 35 + 58 = 227120
Total proportion of water is 13 + 25 + 38 = 133120
Proportion of milk and water in the solution is = 227 : 133
Question 29Rs 4830 is divided among Abhishek, Dishant and Prashant such that if Abhishek’s share diminishes by Rs 5, Dishant’s share diminishes by Rs 10 and Prashant’s share diminishes by Rs 15, their shares will be in the ratio 5:4:3. Find the Dishant’s original share?1610
201024101590Question 29 Explanation: Let actual share of Abhishek, Dishant and Prashant be A, D , P respectively
A + D + P = 4830
Hence, A’s, D’s and P’s share are diminished by Rs 5, Rs 10 and Rs 15, their net share will be Rs.4800
Dishant’s diminished share = 412 × 4800 = Rs 1600
Hence, Dishant actual share = Rs 1600 + Rs 10 = Rs 1610
Question 30The ratio of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. The value of n is?15
253540Question 30 Explanation: Sum of squares of first n natural numbers
= ∑n2 = n(n + 1)(2n + 1)6
Squares of sum of first n natural numbers
= (∑n)2 = n(n + 1)2 × n (n + 1)2
Now the ratio is
= n(n +1)(2n + 1) 6 : n (n+1) 2 × n (n+1) 2= 17 : 325
⇒ (2n + 13)(n (n + 1) 2) = 17325
⇒2(2n + 1)3n(n + 1) = 17325
⇒ 650 (2n + 1) = 51n (n + 1)
⇒ 1300n + 650 = 51n2 + 51n
⇒ 51n2 − 1300n + 51n − 650 = 0
⇒ 51n2 − 1249n − 650 = 0
Upon solving the above equation, we get,
n = 25, − 0.5098
Out of these two,
n = 25 is there in the solution
Question 31Two men, sitting on the dining table. One man has 7 eggs and other had 5 eggs. A third man passing by requested them to share their food in return for money. The three of them shared the eggs equally and the third traveler paid the other two a total of Rs 24. Find the difference between the amounts received by first two men?18121615Question 31 Explanation: As the two men had a total of 12 = ( 7 + 5) eggs, also they agreed to share eggs in such a manner that
all three of them got an equal number of eggs
So each of them must have got 4 = (123) eggs
The first and the second man must have given 3 = (7 − 4) eggs and 1= (5 − 4) egg to the third man
Hence, the ratio of their share is 3 : 1
Now, money has to be distributed in the ratio of their contribution. As total money paid by the stranger is Rs. 24
Hence the first and the second man get Rs 18 = (24 × 33 + 1) and Rs 6 = (24 × 13 + 1) respectively
The 1st man gets Rs 12 = (18 − 6) more than the second
Question 32A, B and C play cricket. A‘s runs are to B‘s runs and B‘s runs are to C‘s as 3:2. They get altogether 342 runs. How many runs did A make?162
10872NoneQuestion 32 Explanation: A : B = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4 (making B equal)
Therefore, A : B : C = 9 : 6 : 4
Therefore, the runs made by A = 919 × 342 = 162
Question 33The most economical speed for this journey is?20 km/hr
30 km/hr
35 km/hr
40 km/hr
Question 33 Explanation: Cost = K2 ×speed2[ Where k is constant]
64 = k × 16 × 16
k = 1/4
Cost = speed2/4
Total cost = (speed2 / 4 + 400 ) x 100 / speed
using options, putting different values of speed, we find speed = 40km/hr to be most economicalQuestion 34The total cost for the journey at this most economical speed is?Rs. 8000
Rs. 6000Rs. 10,000Rs. 11,000Question 34 Explanation: E=ks2
⇒ E= 64 and S = 16
K=1/4
Total cost =1/4 × s2t + 400t
=14 × s 2t + 400t
Most economical speed, checking options we get most economical speed at 40km/hr
Total cost at 40km/hr
= ¼ x 40 2 + 400 ( 400 / 40)
= Rs. 8000Question 35Points A and B are both in the line segment PQ and on the same side of its midpoint. A divides PQ in the ratio 2:3, and B divides PQ in the ratio 3:4. If AB=2, then the length of PQ is?70758085Question 35 Explanation: Let PA = 2x and AB = 3x
and PB = 3y and BQ = 4y
PB : BQ = 3 : 4
PA : QA = 2 : 3
PQ = 5x = 7y
x = 7 / 5 …..(i)
From equation (i) and (ii),
Now, AB = PQ − PA − BQ =7y − 4y −2x
⇒ 3y − 2x = 2 ————– (ii)
y = 10 and Hence, PQ = 70
Question 36Three beakers have capacity of 250ml, 650ml and 200ml. 682 ml of Juice is poured into them so that the same fraction of each is filled. The volume filled in the largest beaker will be?415 ml
403 ml400 ml424 mlQuestion 36 Explanation: As the beaker filled by the same fractions,
p250 = q650
= r200
= p + q + r250 + 650 + 200
Thus p + q + r = 682
⇒q = 403 ml Question 37The total surface area of a solid iron cube and a solid aluminium cuboid are the same. The length, breadth and height of the cuboid are in the ratio 1:2:4. Both are melted together in a vessel. What is the ratio of iron and aluminium in the resultant mixture?
(14/3)3/2:8
8:(14/3)3/2
(3/14)3/2:8
8:(3/14)3/2
Question 37 Explanation: lbh = 2 (lb + bh + hl)=1 : 2 : 4 = 2l , h = 4l = 2×(2l2 + 8l2 + 4l2)=28l2
= (14/3)3/2l3 = (14/3)3/2:8Question 38The monthly salaries of two persons are in the ratio of 4:7. If each receives an increase of Rs.25 in the salary, the ratio is altered to 3:5. Find their respective salaries?120 and 210
80 and 140180 and 300200 and 350Question 38 Explanation: Let the salaries be 4x and 7x
Therefore, 4x + 257x + 255(4x + 25)20x + 125x = 35 = 3(7x + 25) = 21x + 75 = 50
Therefore, their salaries are 4 × 50 and 7 × 50 i.e., 200 and 350
Question 39On a certain day, the ratio of the passenger in the 1st class and the second class travelling by train is 1:3. The ratio of the fares collected from each first class and second class passengers is 30:1. If the total amount collected from all the passengers is Rs 1,320. Find the amount in Rs, collected from the second class passengers?240
360480120Question 39 Explanation: Let the number of passengers travelling by first class and second class be x and 3x respectively
Lets the fares collected from each of the first class and second class passengers be 30y and y respectively
Hence
x(30y) + 3x(y) = 30xy + 3xy = 33xy = 1320
xy = 40
Total amount collected from the second class
= 3xy = 3 × 40 = Rs 120
Question 40By mistake, instead of dividing Rs 117 among three persons P, Q and R in the ratio (12,13,14), it was divided in the ratio 2:3:4. Who gains the most and how much?28352527Question 40 Explanation: Ratio 12,13,14 is equivalent to 6 : 4 : 3
So, in case of correct distribution, P would have got,
=> 117 × 66 + 4 + 3 = Rs. 54
Q would have got, = 117 × 46 + 4 + 3 = Rs. 36
and R would have got, = 117 × 36 + 4 + 3 = Rs. 27
But actually the money was divided in the ratio 2 : 3 : 4 and shares of P, Q and R in this case would be
For P, = 117 × 22 + 3 + 4 = Rs. 26
For Q, = 117 × 32 + 3 + 4 = Rs. 39,
and for R, = 117 × 42 + 3 + 4 = Rs. 52
Thus P gains, = 54 − 26 = 28,
Q gains, = 36 − 39 = −3 (loss)
and R gains, = 27 − 52 = −25 (loss)
Thus, P gains the most Rs. 28
Question 4120 of the students in a class failed in an examination. Out of the students who failed, 75 were males. Male students who failed constitute 90 of the economically poor students in the class. What is the ratio of the number of economically poor students to the number of students in the class?1 : 41 : 5
5 : 61 : 6Question 41 Explanation: Let the total number of students in the class be ‘t’
Let total number of students in the class who are economically poor be ‘p’
Total number of students who failed = t5
Total number of male students who failed
= 34 × t5 = 9p10
⇒ pt = 16
⇒ Number of economically poor studentsNumber of Students = 16 = 1 : 6
Question 42The present ages of A and B are as 6:4. Five years ago their ages were in the ratio 5:3. Find their present ages?42, 28
36, 2430, 2025, 15Question 42 Explanation: Go from the choices
Choice (C) 30 and 20 are in the ratio of 6 : 4
Five years ago their ages would be 25 and 15 which are in the ratio 5 : 3
Hence choice (C) is the right answer
Question 43A, B and C enter into a partnership by investing Rs.3600, Rs.4400 and Rs.2800. A is a working partner and gets a fourth of the profit for his services and the remaining profit is divided amongst the three in the rate of their investments. What is the amount of profit that B gets if A gets a total of Rs. 8000?4888.88
9333.33
40003666.66Question 43 Explanation: Let x be the profit
Their investment ratio = 3600 : 4400 : 2800 = 9 : 11 : 7
A’s profit of Rs. 8000 = 14 × x + 13 × 34 × x =12 × x
x = Rs 16,000
Therefore B’s profit = 1127 × 34 × 16,000 = Rs 4888.88
Question 44A noodles merchant buys two varieties of noodles the price of the first being twice that of the second. He sells the mixture at Rs 17.50 per kilogram thereby making a profit of 25. If the ratio of the amounts of the first noodles and the second noodles in the mixture is 2:3, then the respective costs of each noodles are?Rs 20, Rs 10
Rs 24, Rs 12
Rs 16, Rs 8
Rs 26, Rs 13
Question 44 Explanation: Let the price of one noodles = k
⇒ the price of other noodle = k2
Price of 1 kg = 2k5 + 35 × k2 = 7k10
But CP = 17.50 × 100125 = 14
⇒ 7k10 = 14
⇒ k = 20
So price of the noodles’s are 20 and 10
Question 45In a house, there are dogs, cats and parrot in the ratio 3:7:5. If the number of cats was more than the number of dogs by a multiple of both 9 and 7, what is the minimum of pets in the house?945630252238Question 45 Explanation: If three kinds of pets are taken be 3k,7k and 5k respectively,
Then 7k − 3k = 63p (where p is any positive integer)
As the number is a multiple of both 9 and 7, it has to be multiple of 63
⇒ k = 63p4
Minimum value of p for which k is a natural number is 4
Thus, k=63
Hence, the number of pets = 15k = 945
Question 46There are N numbers of apples in the house, in which four people are lived. If the first men woke up and divided the apples into 5 equal piles and found one extra apple. He took one of those piles along with the extra apple and hid them. He then gathered the 4 remaining piles into a big pile, woke up the second person and went to sleep. Each of the other 3 persons did the same one by one i.e. divided the big pile into 5 equal piles and found one extra apple. Each hid one of the piles along with the extra apple and gathered the remaining 4 piles into a big pile. If N>1000, what could be the least value of N?1249
102312021246Question 46 Explanation: Suppose N=5x + 1
A took (x + 1) biscuit
Now 4x is of the form 5y + 1 then x must be in the form 5z + 4
⇒4(5z + 4) = 5y + 1
⇒ y = 4z + 3 and x = 5z + 4
The ratio of number of biscuits that A and B took is
[(5z + 4) +1] : [(4z + 3) + 1] = 5 : 4
So, we can say that any two successive persons A, B, C and D take coins in the ratio of 5 : 4
Let the number of biscuits that A, B, C and D took be a, b, c and d respectively
a : b = b : c = c : d = 5 : 4
a : b : c : d = 125 : 100 : 80 : 64
⇒ a = 125k
⇒ x = 125k − 1 and N = 5x + 1 = 625k − 4
As, N>1000, the least value of N is when k = 2
N = 1246
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