Question 1

On mixing two classes of students having average marks 25 and 40 respectively, the overall average obtained is 30 marks. Find the number of students in first class, if the second class has 30 students.?

Accepted Answer

Students in the first class / Students in second class = (40 - 30)/(30 - 25) = 10/5 = 2/1 ∴ Students in first class = 2 x 30 = 60

Question 2

In a mixture of 60 L, the ratio of milk and water is 2 : 1. If the ratio of milk and water is to be 1 : 2, then the amount of water to be further added must be?

Accepted Answer

Milk = (2/3) x 60 = 40 L Water = (1/3) x 60 = 20 L Water added = W L Now, 40/(20 + W) = 1/2 ⇒ W = 60 L

Question 3

In a certain school, the ratio of boys to girls is 7 : 5. If there are 2400 students in the school, then how many girls are there in the school?

Accepted Answer

Let the number of boys and girls are 7k and 5k, respectively. Given, total number of students = 2400 ⇒ 7k + 5k = 2400 ⇒ 12k = 2400 ⇒ k = 200 ∴ Required number of girls = 5k = 5 x 200 = 1000

Question 4

If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14, then find c?

Accepted Answer

Let a + b = 6k, b + c = 7k, c + a = 8k ...(i) and a + b + c = 14 ...(ii) From Eq. (i), a + b + b + c + c + a = 6K + 7K + 8K ⇒ 2(a + b + c) = 21K ⇒ 2 x 14 = 21K ⇒ K = 28/21 = 4/3 ⇒ a + b 6k = = 6 x 4/32 = 8 Subtracting Eq. (iii) from Eq. (ii), we get (a + b + c) - (a + b) = 14 - 8 = 6

Question 5

One - half of a certain number is equal to 65% of the 2nd number. Find the ratio of 1st to 2nd number.

Accepted Answer

Let 1st number = x and 2nd number = y According to the question 1/2 of x = 65% of y ⇒ x/y = 130/100 = 13/10 ∴ x : y = 13 : 10

Question 6

The ratio between two number is 3 : 4. if each number is increased by 3, the ratio becomes 4 : 5. Find the differences between the numbers.

Accepted Answer

Let the number be 3k and 4k. According to the question, (3k + 3)/(4k+ 3) = 4/5 ⇒ 5(3k + 3 ) = 4(4k + 3) ⇒ 15k + 15 = 16k + 12 ∴ k = 15 - 12 = 3 ∴ Difference between the numbers = (4k - 3k) = k = 3

Question 7

From each of two given numbers, half the smaller number is subtracted. After such subtraction, the larger number is 4 times as large as the smaller number. What is the ratio of the numbers?

Accepted Answer

Let the smaller number = M and the greater number = N According to the question , (N - M/2) = 4(M - M/2) ⇒ N - M/2 = 4M/2 ⇒ N = 2M + M/2 ⇒ N = 5M/2 ∴ N : M = 5 : 2

Question 8

Two number are in the ratio of 2 : 3. If 9 is added to each number, they will be in the ratio 3 : 4. What is the product of the two numbers?

Accepted Answer

Let the number be M and N According to the question. M/N = 2/3 ⇒ 3M = 2N ⇒ 3M - 2N = 0 ...(i) And (M + 9)/(N + 9) = 3/4 ⇒ 4M + 36 = 3N + 27 ⇒ 4M - 3N = -9 ...(ii) Multiplying Ex. (i) by 4 and Eq. (ii) by 3 and subtracting, we get N = 27 Now, putting N = 27 in Eq. (i), we get 3M = 54 ⇒ M = 18 ∴ Product of the given numbers = 27 x 18 = 486

Question 9

Weekly income of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves ₹ 300 per week, then the weekly income of the first person is?

Accepted Answer

Let the income of two persons are 7k and 3k Expenditure of first person = 7k - 300 Expenditure of second person = 3k - 300 According to the question, (7k - 300)/(3k - 300) = 5/2 ⇒ 14k - 600 = 15k - 1500 ∴ k = 900 Income of first person = 7k = 7 x 900 = ₹ 6300

Question 10

Amit and Sudesh have invested in the ratio of 4 : 7. If both invested a total amount of ₹ 49500, then find the investment of Sudesh?

Accepted Answer

Given total amount = ₹ 49500 Let part of Amit's investment = 4k and part of sudesh's investment = 7k According to the question 4k + 7k = 49500 ⇒ 11k = 49500 ⇒ k = 49500/11 ∴ k = 4500 Hence investment of sudesh = 7k = 7 x 4500 = 31500

Question 11

A bag contains ₹ 1, 50 paise and 25 paise coins in the ratio of 8 : 9 : 11. If the total money in the bag is ₹ 366, then find the number of 25 paise coins?

Accepted Answer

Let number of ₹ 1 coins = 8k Number of 50 paise coins = 9k Number of 25 paise coins = 11k According to the question, 8k + 9k/2 + 11k/4 = 366 ⇒ 32k + 18k + 11k = 1464 ⇒ 61k = 1464 ∴ k = 1464/61 = 24 ∴ Number of 25 paise coins = 11k = 11 x 24 = 264

Question 12

If sum of ₹ 1664 is divided between P and Q in the ratio of 1/3 : 1/5, then find P's share?

Accepted Answer

Given that P's share : Q 's share = 1/3 : 1/5 = 5 : 3 Here, a = 5, b = 3, N = 1664 P's share = a/(a + b) x N ∴ = 5/(5 + 3) x 1664 = (5/8) x 1664 = ₹ 1040

Question 13

The marks of 3 students A, B and C are in the ratio 10 : 12 : 15. If the maximum marks of the paper are 100, then the marks of B cannot be in the range of?

Accepted Answer

Let the marks of A, B and C are 10k, 12k and 15k, respectively. Let k = 6 ∴ Maximum marks of C can be = 15 x 6 = 90 So, maximum marks of B can be = 12 x 6 = 72 As the marks are fixed and they cannot exceed the maximum marks. So, the marks of B cannot be in the range of (80 - 90) ie B cannot score above 80.

Question 14

Brother A and B had some saving in the ration 4 : 5. They decided to buy a gift for their sister, sharing the cost in the ratio 3 : 4, After they bought, A spent two- third of his amount, while B is left with ₹ 146, Then the value of the gift is?

Accepted Answer

let the saving of A and B are 4M , 5M and the share in cost of gift are 3N, 4N respectively According to the question for A, 4M - 3N = (2/3) x 4M ⇒ M = 9N/4.............(i) For B 5M - 4N = 145 ⇒ 5 x (9N/4) - 4N = 145 [by Eq. (i)] ∴ N = 20 ∴ Cost of gift = 3N + 4N = 7 x 20 = ₹ 140

Question 15

A sum of the ₹ 300 is divided among P, Q and R in such a way that Q gets ₹ 30 more than P and R gets ₹ 60 more then Q. Then, ratio of their shares is?

Accepted Answer

Let the share of P = x Then, Q's share = x + 30 and R's share = (x + 30) + 60 = x + 90 Sum of money with P, Q and R = 300 ∴ x + (x + 30) + (x + 90) = 300 ⇒ 3x + 120 = 300 ∴ x = (300 - 120)/3 = 60 ∴ Required ratio = 60 : (60 + 30) : (60 + 90) = 2 : 3 : 5

Question 16

Salary of Mr. X is 80% of the salary of Mr. Y and salary of Mr. Z is 120% of the salary of Mr. X. What is the ratio between the salaries of X, Y and Z respectively?

Accepted Answer

Let Y's salary = 100 ∴ X's salary = 80 and Z's salary = 80 x (120/100) = 96 ∴ Required ratio = 80 : 100 : 96 = 20 : 25 : 24

Question 17

If the position of the digits of a two-digit number are interchanged, the number newly formed is smaller than the original number by 45. Also, the ratio of the new number to the original number is 3 : 8, What is the original number?

Accepted Answer

According to the question. 8N - 3N = 45 ⇒ 5N =45 ∴ N = 45/5 = 9 ∴ Orignal number = 8N = 8 x 9 = 72

Question 18

₹ 5625 are divided among A, B and C so that A receives 1/2 as much as B and C together receive and B receives 1/4 as much as A and C together receive. Find the sum of shares of A and B.

Accepted Answer

Accoridng to rhe question A = ( B + C)/2 ⇒ B + C = 2A ⇒ A + B + C = 3A (adding A on both sides) ∴ 3A = 5625 ∴ A = 5625/3 = ₹ 1875 ....(i) Again from question B = (A + C)/4 ⇒ A + C = 4B ⇒ A + B + C = 5B (adding B on both sides) ⇒ 5B = 5625 ∴ B = 5624/5 = ₹ 1125 ...(ii) From (i) and (ii) ⇒ A + B = 1875 + 1125 = ₹ 3000

Question 19

₹ 710 were divided among A, B and C in such a way that A had ₹ 40 more than B and C had ₹ 30 more than A. How much was C's share?

Accepted Answer

Let B gets x. Then, A gets (x + 40) and C gets (x + 70). According to the question, x + 40 + x + x + 70 = 710 ⇒ 3x = 710 - 110 = 600 ∴ x = 600/3 = 200 ∴ C's share = 200 + 70 = ₹ 270

Question 20

The ratio of 1st and 2nd classes train fairs between two stations is 3 : 1 and that of the number of passengers travelling between these stations by 1st and 2nd classes is 1 : 50. If on a particular day, ₹ 2650 be collected from the passengers trave…

Accepted Answer

Ratio of the amounts collected from 1st and 2nd classes fairs = (3 x 1) ; (1 x 50) = 3 : 50 ∴ Amount collected from 2nd class Passengers = 2650 x (50/53) = ₹ 2500

Ratio and Proportion Questions