The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs. 1250, find their incomes.

Given:

The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16 and each saves Rs. 1250.

To do:

We have to find their incomes.

Solution:

Let the incomes of X and Y be $8x$ and $7x$ respectively. Let the expenditures of X and Y be $19y$ and $16y$ respectively.  

We know that,

Savings $=$ Income $-$ Expenditure

Therefore,

Savings of X $=8x-19y$

Savings of Y $=7x-16y$

According to the question,

$8x-19y=1250$.....(i)

$7x-16y=1250$.....(ii)

Multiplying equation (i) by 7 and equation (ii) by 8, we get,

$7(8x-19y)=7(1250)$

$56x-133y=8750$....(iii)

$8(7x-16y)=8(1250)$

$56x-128y=10000$....(iv)

Subtracting (iii) from (iv), we get,

$56x-128y-(56x-133y)=10000-8750$

$56x-56x-128y+133y=1250$

$5y=1250$

$y=\frac{1250}{5}$

$y=250$

$7x-16(250)=1250$    (From (ii))

$7x-4000=1250$

$7x=4000+1250$

$7x=5250$

$x=\frac{5250}{7}$

$x=750$

$\Rightarrow 8x=8(750)=6000$

$\Rightarrow 7x=7(750)=5250$

Therefore, the incomes of X and Y are Rs. 6000 and Rs. 5250 respectively.

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Updated on: 10-Oct-2022

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