Rs.5887 is divided between Shyam and Ram, such that Shyam's share at the end…
2024
Rs.5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.
- A.
Rs 1087
- B.
Rs 2087
- C.
Rs 3087
- D.
Rs 4087
Attempted by 20 students.
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Correct answer: C
Solution: Let Shyam's share be S and Ram's share be 5887 − S.
Shyam's amount after 9 years equals Ram's amount after 11 years at 5% compounded annually, so:
Write the equation: S*(1.05)^9 = (5887 − S)*(1.05)^11.
Divide both sides by (1.05)^9: S = (5887 − S)*(1.05)^2 = 1.1025*(5887 − S).
Bring S terms together: S + 1.1025 S = 1.1025 × 5887 ⇒ 2.1025 S = 6490.4175.
Solve for S: S = 6490.4175 ÷ 2.1025 = 3087.
Check: Ram's share = 5887 − 3087 = 2800. Then 2800*(1.05)^11 = 2800*(1.05)^9*(1.05)^2 = 3087*(1.05)^9, so the matured amounts are equal.
Answer: Shyam's share = Rs 3087.