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A man wants to invest Rs. 8425 in bank account of his two daughters whose age are 24 years and 28 years in such a way that they will get equal amount on age of 40 years at the rate of 33.3% compounded annually. Find the share of elder daughter.1. Rs. 64002. Rs. 64643. Rs. 54004. Rs. 70005. Rs. 6482 |
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Answer» Correct Answer - Option 1 : Rs. 6400 Given: Total amount to invest = Rs. 8425 Ages of sons are 24 years and 28 years. Formula used: A = P(1 + r/100)n Where, A = Amount P = Principal r = Rate n= time Calculation: Let Principal of younger daughter be (P1) And, Let Principal of elder daughter be (P2) Time of elder daughter = (40 – 28) years = 12 years Time of younger daughter = (40 – 24) years = 16 years Rate = 33.3% = (100/3)% According to the question: Younger daughter = Elder daughter P1(1 + r/100)n = P2(1 + r/100)n ⇒ P1[1 + (100/3 × 100)]16 = P2[1 + 100/3 ×100)]12 ⇒ P1(4/3)16 = P2(4/3)12 ⇒ P1/P2 = [(4/3)12/(4/3)16] ⇒ P1/P2 = [1/(4/3)4] ⇒ P1/P2 = (3/4)4 ⇒ P1/P2 = 81/256 ⇒ P1 : P2 = 81 : 256 Now, again let P1 be 81x Let P2 be 256x Total principal = (81x + 256x) = Rs. 337x Again, ⇒ 337x = 8425 ⇒ x = 8425/337 P1 = 256x = 256 × (8425/337) = Rs. 6400 ∴ The share of elder daughter is Rs. 6400. |
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