Question

The incomes of X and Y in the ratio 8 : 7 and their expenditure are in the ratio 19: 16. If each saves Rs. 2500, find their income.

Answer 1

Let income of X be 8a and income of Y be 7a




$\mathbf{ We \: \: know , \: Income - saving = expenditure}$



Hence,

$\bold{ \frac{ salary \: of \:X - saving \: of \: X}{salary \: of \: Y \: - saving \: of \: Y}= \frac{19}{16} }$




Hence,

$\longrightarrow \: \: \: \frac{8a - 2500}{7a - 2500} = \frac{19}{16} \\ \\ \rightarrow \: 16(8a - 2500) = 19(7a - 2500)$



=> 128a - 40000 = 133a - 47500


=> 47500 - 40000 = 133a - 128a


=> 7500 = 5a


=> 1500 = a





$\mathbf{ Due \: to \: this, Salary \: \: of \: \: X = 8a = 8( 1500 ) = 12000} \\ \\ \\ \\ \mathbf{Salary \: \: of \: \: Y = 7a = 7( 1500 )= 10500}$

Answer 2

Income of x = 8a & income of Y = 7a

8a - 2500/7a - 2500 = 19/16

128a - 40000 = 133a - 47500

5a= 7500

a = 1500

Income of x = 8a = 8 x 1500 = Rs. 12000

Y = 7a = 7 x 1500 = Rs. 10500

hope it help u