Math, asked by ScientistKhushi, 1 year ago

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

Answers

Answered by Rvbest
298
you can solve the ans by using substitution and elimination method
Attachments:
Answered by Golda
319
Solution :-

Let the income of X be Rs. 'a' and his expenditure be Rs. 'b'.

And, income of Y be Rs. 'c' and his expenditure be rs. 'd'.

Therefore,

a/c = 8/7 

⇒ a = 8c/7

Similarly,

b/d = 19/16

⇒ b = 19d/16

Savings of X = a - b

⇒ 1250 = 8c/7 - 19d/16

Taking L.C.M. of the denominators and then solving it, we get.

⇒ 1250 = (128c - 133d)/112

⇒ 128c - 133d = (1250*112)

⇒ 128c - 133d = 140000 .............(1)

Savings of Y = c - d

⇒ c = 1250 + d ............(2)

Substituting (2) in (1), we get.

⇒ 128*(1250 + d) - 133d = 140000

⇒ 160000 + 128d - 133d = 140000

⇒ 128d - 133d = 140000 - 160000

⇒ - 5d = - 20000

⇒ 5d = 20000

⇒ d = 20000/5

⇒ d = 4000

Putting d = 4000 in (2), we get.

Now, c = 1250 + 4000
 
⇒ c = 5250

Now, putting c =  5250 in a = 8c/7

⇒ a = (8*5250)/7

⇒ a = 42000/7

⇒ a = 6000

And, b = 6000 - 1250 

b = 4750

Hence, the income of X is Rs. 6000 and income of Y is Rs. 5250

Answer.
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