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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.