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20) The incomes of X and Y are in the ratio of 8:7 and their expenditures are in the ratio 19: 16. If each saves 1250,find their incomes.by ue naii alnuins olglal rate or waikingthe whddone the9, A train o |
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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 |
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