Learn to solve ratio and proportion in a jiffy

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions on the ratio and proportion topic that will help you in your preparation for the State government recruitment jobs. The monthly incomes of two persons are in the ratio of 4 […]

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

The monthly incomes of two persons are in the ratio of 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves 50 a month, then what are their monthly incomes?

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a) Rs 200, Rs 300 b) Rs 250, Rs 350 c) Rs 125, Rs 150 d) Rs 400, Rs 500

Ans: d

Solution: Let the income of two persons be Rs 4x and
Rs 5x and their expenses be Rs 7y and Rs 9y respectively.
Then, 4x – 7y = 50 (i)
And 5x – 9y = 50 (ii)
On solving Eqn. (i) and (ii), we get x = 100 and y = 50
⇒The income of persons are Rs 400 and Rs 500

Gajodhar and Manohar’s salary ratio was 3 : 4 one year ago. The ratio of their individual salaries between last year’s and this year’s salaries are 4 : 5 and 2 : 3 respectively. At present the total of their salary is Rs.4160. The present salary of Gajodhar is?

a) 1000 b) 1200 c) 1400 d) 1600

Ans: d

Solution: Let the salaries of Gajodhar and Manohar one year before be a, b respectively
and now be c, d respectively.
a : b = 3 : 4
a : c = 4 : 5
b : d = 2 : 3
It is given that c d = 4160
a/b=3/4, a/c = 4/5, b/d= 2/3
a/c x d/b, 4/5 x 3/2
a x d / b x c = 6/5 or d/c x 3/4 = 6/5
c/d = 5/8, c d = 4160
c = 5/13 x 1460 = 1600

Swetha is 10 years younger than her sister Seema who was 14 years old when her mother was 34 years old. The ratio of the ages of the mother and Swetha after 6 years will be 2 : 1. After how many years the average of their ages will be 39.33 years?

a) 2 years b) 5 years c) 3 years d) 6 year

Ans: a

Solution: Let the present age of Seema be x years
Swetha’s present age = x – 10
When Seema was 14 years, mother was 34 years. So, when Seema is x years, mother will be = 34 – 14 x
Mother’s present age = 20 x
According to the question,
x 20 6/x-10 6 = 2/1
x 26/x-4 = 2/1
x = 34 years
Seema’s age = 34 years Swetha’s age = 24 years
Mother’s present age = 54 years
Average = 34 24 54/ 3 = 37.33 years
After 2 years, Seema’s age = 36 years, Swetha’s age = 26 years, Mother’s age = 56 years Average after 2 years,
Average = 30 20 50/ 3 = 39.33 years

A 4 years ago, the ratio of the age of two friends Virat and Dinesh was 3 : 1. Their present age differ by 4 years. Find the average of their ages, after 2 years?

a) 10 years b) 11 years c) 12 years d) 13 years

Ans: a

Solution: Let the age of Virat and Dinesh be V and D respectively
Given that,
V – D = 4
V = D 4 …(i)
4 years ago,
Virat will be (V – 4) years and
Dinesh will be (D – 4) years
(V – 4) : (D – 4) = 3 : 1
Using (I), we get D = 6 and V = 10 years
Average of their ages after 2 years
V 2 D 2/ 2 years = 10

To be continued….