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.
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you can solve the ans by using substitution and elimination method
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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.
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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