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 Rs. 1250, find their incomes.
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Answer 1

Answer :-

• Income of X = 6000 Rs
• Income of Y = 5250 Rs

Given :-

• Ratio of incomes of X and Y is 8 : 7
• Ratio of expenditures of X and Y is 19 : 16
• each person saves Rs. 1250

To find :-

• Incomes of X and Y

Solution :-

Let, incomes of X and Y be

8 a and  7 a   respectively

and,

Let, their expenditures be

19 b  and  16 b   respectively

then,

→  8 a - 19 b = 1250

→  8 a = 1250 + 19 b

→ a = ( 1250 + 19 b ) / 8   ....eqn (1)

Also,

→  7 a - 16 b = 1250

using eqn (1)

→ 7 (( 1250 + 19 b ) / (8)) - 16 b = 1250

taking LCM in LHS

→ ( 7 ( 1250 + 19 b ) - 128 b ) / 8 = 1250

cross multiplying

→  8750 + 133 b - 128 b = 10000

→  5 b = 1250

→ b = 1250 / 5

→ b = 250

putting value of b is eqn (1)

→ a = ( 1250 + 19 b ) / 8

→ a = ( 1250 + 19 ( 250 ) ) / 8

→ a = ( 1250 + 4750 ) / 8

→ a = 6000 / 8

→ a = 750

Therefore,

Income of X = 8 a

                    = 8 ( 750 )

Income of X = 6000 Rs

Income of Y = 7 a

                    =  7 ( 750 )

Income of Y = 5250 Rs.