Question

The ratio of incomes of Anubhav and Abhinav is 5 : 7. Their expenses are in the ratio of 3.2.
An increase of Rs 500 in the expenses of Abhinay and an decrease of Rs 100 in the expenses of Anubhav makes their saving Rs 500 each. Find their incomes.
(Rewa, 2007)
[Ans. Rs1,000 and Rs 1,400]​

Answer 1

Answer:

rs1000or rs1400 hAi guarrented

Answer 2

Income of anubhav is Rs 1000 and income of abhinav is Rs 1400

Solution:

Given that,

The ratio of incomes of Anubhav and Abhinav is 5 : 7

Let the income of Anubhav be 5x

Let the income of Abhinav be 7x

Their expenses are in the ratio of 3 : 2

Let the expenditure of Anubhav be 3y

Let the expenditure of Abhinav be 2y

An increase of Rs 500 in the expenses of Abhinay and an decrease of Rs 100 in the expenses of Anubhav makes their saving Rs 500 each

As per this condition,

New expenditure of Abhinav = 2y + 500

New expenditure of Anubhav = 3y - 100

Saving for both is now 400

We know that,

Saving = Income - expenditure

Therefore,

5x - (3y - 100) = 500

5x - 3y + 100 = 500

5x - 3y = 400 -------- eqn 1

Also,

7x - (2y + 500) = 500

7x - 2y - 500 = 500

7x - 2y = 1000 ------- eqn 2

Solve eqn 1 and eqn 2

Multiply eqn 1 by 2

10x - 6y = 800 ------- eqn 3

Multiply eqn 2 by -3

-21x + 6y = -3000 ------- eqn 4

Add eqn 3 and eqn 4

10x - 6y - 21x + 6y = 800 - 3000

-11x = -2200

x = 200

Thus,

Income of anubhav = 5x = 5(200) = 1000

Income of abhinav = 7x = 7(200) = 1400

Thus income of anubhav is Rs 1000 and income of abhinav is Rs 1400

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