# Ratio and Proportion - 1

Directions (Qs. 1 - 14): Study the following questions carefully and choose the right answer.

1. Anmol had 10 paise, 25 paise and 50 paise coins in the ratio of 10 : 8 : 9 respectively. After giving Rs.20 his mother he has Rs.40. How many 50 paise coins did he have?

A) 72     B) 60    C) 54     D) 35    E) 21

Explanation: Total money = 20 + 40 = Rs.60 In this question the total money is given so we need to multiply the value of the coins in the ratio. 10 × 0.10x + 8 × 0.25x + 9 × 0.50x = 60

x + 2x + 4.5x = 60

x = 8

Number of 50 paise coins = 9 × 8 = 72

Ans: A

2. Three numbers A, B and C are in the ratio of 12 : 15 : 25. If sum of these numbers is 312, ratio between the difference of B and A and the difference of C and B is....

A) 3 : 7    B) 10 : 3    C) 3 : 10     D) 5 : 7     E) None of these

Explanation: Let the number A, B and C be 12a , 15a and 25a respectively. Then from the question 12a + 15a + 25a = 312

Ans: C

3. The ratio of Nicotine to Heroine in four types of drugs of equal quantity is 2 : 3, 3 : 7, 4 : 11 and 11 : 9 respectively. The four drugs are mixed together. What is the ratio of Nicotine to Heroine after mixing?

A) 213 : 91    B) 418 : 189     C) 91 : 149    D) 149 : 81     E) None of these

Explanation: Let the quantity of each drugs be ‘a’. Then quantity of nicotine after mixing is

4. Out of three positive numbers, the ratio of the first and the second numbers is 3 : 4 that of the second and the third numbers is 5 : 6 if the product of the second and the third numbers is 4320. What is the sum of three numbers?

A) 177      B) 165      C) 185     D) 160    E) None of these

Explanation: Ratio of 1st and 2nd numbers = 3 : 4

Ratio of 2nd and 3rd numbers = 5 : 6

Let the 2nd number = 5x, third number = 6x

Product of 2nd and 3rd numbers = 4320

5x × 6x = 4320 ⇒ x 2 = 144 ⇒ x = 12

2nd number = 60, 3rd number = 72,

1st number = 60/4 X 3 = 45

Sum of three numbers = 60 + 72 + 45

= 177

Ans: A

5. The cost price of 2 shirts and 3 jeans is Rs.2200 and the cost price of 2 jeans and 4 shirts is Rs.2400. Find the ratio between the cost price of the jeans and the shirt.

A) 8 : 9    B) 10 : 7    C) 6 : 5    D) 11 : 10    E) None of these

Explanation: Let the cost price of one shirt = Rs.x, and cost price of one jeans = Rs.y According to the question,

2x + 3y = 2200 .... (1)

2y + 4x = 2400

2x + y = 1200 .... (2)

After solving these 2 equations we get

x = Rs.350, y = Rs.500

Ratio = 500 : 350 = 10 : 7

Ans: B

6. Three numbers are in the ratio 5 : 6 : 7. If the sum of their squares is 990, then the numbers are....

A) 10, 12 and 21    B) 25, 30 and 35     C) 15, 18 and 21     D) 20, 24 and 28     E) None of these

Explanation: Approach I:

Let the numbers be 5x, 6x and 7x

∴ (5x)2 + (6x)2 + (7x)2 = 990

⇒ 25x2 + 36x2 + 49x2 = 990

⇒ 110x2 = 990 ⇒ x 2 = 9 ⇒ x = 3

∴ Numbers = 15, 18 and 21.

Approach II: Pick each of the options. Add unit digits of the squares of unit digit of the numbers given in a particular option and match the resultant unit digit with the unit digit of the given total; 0 in 990.

Squares of the unit digits of the numbers (15, 18, 21) given in option C are 5, 4 and 1 which on addition give us 10 the unit digit of which is 0.

Ans: C

7. The ratio of Sita’s, Riya’s and Kunal’s monthly income is 84 : 76 : 89. If Riya’s annual income is Rs.4,56,000, what is the sum of Sita’s and Kunal’s annual incomes? (In some cases monthly income is used while in other annual income is used.)

A) Rs.11,95,000    B) Rs.9,83,500    C) Rs.1,13,000    D) Rs.10,38,000    E) None of these

Explanation: Ratio of monthly income and ratio of annual income will be the same, ie.

84 : 76 : 89

Applying the rule of proportion, we get

Riya's income in ratio : Riya's total income

: : Sum of Sita's and Kunal's income in ratio

: Sum of Sita's and Kunal's income in value

76 : 456000 : : (84 + 89) : x

∴ Sum of Sita's and Kunal's annual income in value

8. Two numbers are in ratio of 21 : 26. If 8 is added in each, the new numbers are in ratio of 5 : 6. Find the ratio of numbers, if 6 is subtracted from each number.

A) 18 : 23    B) 19 : 25    C) 6 : 7    D) 9 : 16    E) None of these

Explanation: Let the numbers be 21x and 26x.

6(21x + 8) = 5(26x + 8)

126x + 48 = 130x + 40 ⇒ x = 2

So, numbers will be 42 and 52.

If 6 is subtracted, then numbers will be 36 and 46.

Required ratio = 36 : 46. i.e. 18 : 23

Ans: A

9. If A varies directly as B and inversely as C and A = 6, when B = 2 and C= 3, what is the value of A when B = 8 and C = 6?

A) 12     B) 6     C) 18    D) 24     E) None of these

Explanation: Let the constant be x, so putting the first scenario in equation

We can find out A in the second scenario by putting value of x as 9

10. The income of Asaram, Satpal and Rahim in the ratio of 12 : 9 : 7 and their spendings are in the ratio 15 : 9 : 8. If Asaram saves 25% of his income. What is the ratio of the savings of Asaram, Satpal and Rahim?

A) 15 : 18 : 11    B) 5 : 8 : 7    C) 23 : 18 : 11     D) 25 : 16 : 13    E) None of these

Explanation: Income = Expenditure + Saving

Asaram: 12x = 15y + 3x (3x = 25% of 12x)

Satpal: 9x = 9y + (9x − 9y)

Rahim: 7x = 8y + (7x − 8y)

Therefore, 12x − 3x = 15y

11. 60 percent of first number is equal to 40 percent of the second number. What is the respective ratio of the first number to the second number?

A) 2 : 3     B) 21 : 31     C) 7 : 10    D) 4 : 6     E) Can’t be determined

Explanation: Let the first number be x and the second number be y. According to the question,

So, required ratio = x : y = 2 : 3

Ans: A

12. Two numbers A and B are such that the sum of 5% of A and 4% of B is two- third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

A) 4 : 3     B) 3 : 4     C) 1 : 1     D) 2 : 3     E) 5 : 3

Explanation: From the equation, we get

5% of A + 4% of B = 2(6% of A + 8% of B)

⇒ 15% of A + 12% of B = 12% of A + 16% of B

⇒ [15 − 12]% of A = [16 − 12]% of B

⇒ 3% of A = 4% of B

A/B = 4/3 ⇒ A : B = 4 : 3

Ans: A

13. 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?

A) 500    B) 700    C) 120    D) 1000     E) 150

​​​​​​​

Number of women = (720 − 420) = 300.

∴ Number of women to be joined

= (420 − 300) = 120

Ans: C

14. What is the ratio whose terms differ by 40 and the measure of which is 2/7?

A) 12 : 56    B) 16 : 56    C) 23 : 58    D) 25 : 60     E) None of these

Let the ratio be x : (x + 40)

∴ Required ratio is 16 : 56

Smarter Approach: Pick one option and check whether it satisfies the given condition or not. The one that satisfies will be the answer.

Option A: 12/56

gets eliminated because the difference between the terms is not 40

Option B: 16/56

is the correct answer because the difference between the terms is 40 and  its measure is also 2/7

Ans: B

Posted Date : 05-06-2023

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