Question

The incomes of x and y are in the ratio 8:7 and their expenditures are in the ratio 19:16.if each saves ₹1250,find their income.

Answer 1

income is 8aand 7a
expenditure is 19band 16b
saving is 1250
8a-19b=1250
7a-16b=1250
19*7b=1250*7
16*8b=1250*8
133b-128b =1250
5b=1250
b=250
a=750
income of x=6000
income of y=5250

Answer 2

Hey,
Thanks for asking this question.

Suppose income of x = 8P

Since incomes of x and y are in the ration 8:7,

=> Income of y = 7P.

Now suppose expenditure of x = 19E

Since expenditure of x and y are in ration 19:16,

=> Expenditure of y = 16E.

Since each saves Rs 1250,
&
Saving = Income - Expenditure

=> saving of x = 8P - 19Q
=> 8P - 19Q = 1250 --------(1)
&
saving of y = 7P - 16Q
=> 7P - 16Q = 1250 ---------(2)

So multiplying equation (1) by 7
&
multiplying equation (2) by 8,

56P - 133Q = 8750 ---------(3)
56P - 128Q = 10000 -------(4)

Subtracting equation (4) by (3),

56P - 133Q - ( 56P - 128Q ) = 8750-10000
=> -133Q + 128Q = -1250
=> -5Q = -1250
=> Q = - 250

Now after putting value of Q in equation (1),
8P - 19×250 = 1250
=> 8P - 4750 = 1250
=> 8P = 6000
=> P = 750

●●So the income of x = 8P = 6000 Rupees
&
●●Income of y = 7P = 5250 Rupees


■■■ Hope my answer helped.