Ratio and proportion problems made easy

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests. 1. Monthly salaries of A and B are in the ratio 8 : 9 respectively. Monthly expenditure of […]

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

1. Monthly salaries of A and B are in the ratio 8 : 9 respectively. Monthly expenditure of A is 140% more than the monthly savings of B. Monthly expenditure of B is Rs 2,000 more than the monthly expenditure of A. Find the difference in the yearly salaries of A and B, if the monthly savings of A and B are in the ratio 4 : 5 respectively.\
a) Rs 20000 b) Rs 15000 c) Rs 28000 d) None of these
Ans: d
Solution: Let the monthly savings of A and B are Rs 4x and Rs 5x respectively
Monthly expenditure of A = 2.40 × 5x = Rs 12x
Monthly expenditure of B = Rs 12x 2000
So, monthly salary of A = Rs (4x 12x) = Rs 16x
Monthly salary of B = Rs (5x 12x 2000) = Rs (17x 2000)
So, according to the question,
(4x 2x) / (5x 12x 2000) = 8/9
2x / (17x 2000) = 1/9
18x = 17x 2000; x = 2000
So, monthly salary of A = 16 × 2000 = Rs 32000
Monthly salary of B = 17 × 2000 2000 = Rs 36000
Difference in the monthly salaries of A and B = 36000 – 32000 = Rs 4000
Difference in the yearly salaries of A and B = 12 × 4000 = Rs 48000

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2. Shubhash’s age 4 years hence is (x 4) years, Poonam’s age 6 years ago was (y – 6) years. The present age of Poonam is 10 less than twice the present age of Shubhash. Shubhash’s age 5 years hence, will be 5 years less than the present age of Poonam. Find the ratio of the present age of Shubhash to the present age of Poonam.
a) 2 : 3 b) 1 : 3 c) 9 : 10 d) 7 : 8
Ans: a
Solution: Shubhash’s age 4 years hence is (x 4), so his present age is x years.
Poonam’s age 6 years ago is (y – 6), so her present age is y years.
y = 2x – 10 (i)
x 5 = y – 5 …..(ii)
Solving both the equations, x = 20 and y = 30 years
Reqd. ratio = 20/30 = 2 : 3

3. The expenses on food, rent and electricity of a family are in the ratio 5 : 15 : 3. The expenditure on food, rent and electricity is increased by 20%, 10% and 30% respectively. The total expenses of family are thus increased by how much percent?
a) 14 (18/23)% b) 15 (17/23)% c) 12 (18/23)% d) 11 (17/21) %
Ans: a
Solution: The expenses on food, rent and electricity of a family are in the ratio 5 : 15 : 3
respectively.
Increase on food → 20% on 5 i.e., Rs 1
Increase on rent → 10% on 15 i.e., Rs 1.5
Increase on electricity → 30% on 3 i.e., Rs 0.90
Total increase in expenses = Rs (1 1.50 0.90)
Reqd. % = (1 1.50 0.90) × 100 / 5 15 3 = 340 / 23% = 14 (18/23)%

To be continued…

M. Venkat
Director
MVK Publications
Dilsukhnagar
7671002120