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## Ratio And Proportion Problems

Here candidates may check Ratio And Proportion Problems With Solutions. Candidates can prepare for their exams with the help of this Online Test. There are also some Shortcuts are given to solve MCQ. All the questions are well designed by team of recruitmentresult.com students may easily prepare with the help of these questions.

## Ratio And Proportion Problems Test

1. The 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?

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 x 7x) and (110/100 x 8x)

42x/5  and     44x/5

The required ratio =  42x/5 x 44x/5 = 21 : 22.

2. Salaries 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?

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

3. Two 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:

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.

4. In 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?

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.

Then, sum of their values = Rs. (25x/100 + 10 x 2x/100 +5 x 3x/100) = Rs. 60x/ 100

60x/100 = 30 i.e. x = (30 x 100)/60 = 50.

Hence, the number of 5 p coins = (3 x 50) = 150.

5. A 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?

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.

6. Seats 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?

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).

i.e (140/100 x 5x) , (150/100 x 7x) and (175/100 x 8x)

7x, 21x/2 and 14x.

The required ratio = 7x : 21x/2 : 14x

14x : 21x : 28x

2 : 3 : 4.

7. If Rs. 782 be divided into three parts, proportional to 1/2 : 2/3 :3/4 , then the first part is:

Given ratio = 1/2: 2/3 : 3/4 = 6 : 8 : 9.

1st part = Rs. (782 x 6/23) = Rs. 204

8. The 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?

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

Sumit’s present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.

9. If 0.75 : x :: 5 : 8, then x is equal to:

(x x 5) = (0.75 x 8) i.e

x = 6/5 = 1.20

10. In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

Quantity of milk = (60 x 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 2)  = 1/2

20 + x = 80

x = 60.

Quantity of water to be added = 60 litres.

11. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

Let 40% of A = 2/3 B

Then,  40A/100= 2B/3

2A/5 =          2B/3

A/B =  (2/ 3x 5/2) = 5

A : B = 5 : 3.

12. The fourth proportional to 5, 8, 15 is:

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.

13. The 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:

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.

14. A and B together have Rs. 1210. If  of A’s amount is equal to  of B’s amount, how much amount does B have?

4/15 A = 2/5 B

A = (2/5 x 15/4) B

A =     3/2 B

A/B = 3/2

A : B = 3 : 2.

B’s share = Rs. (1210 x 2/5) = Rs. 484.

15. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

Let the third number be x.

Then, 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.

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