Question
Rs. 16,820 is divided between two brothers of age 27 years and 25 years. They invested their money at 5% per annum compound interest in such a way that both will receive equal money at the age of 40 years. The share (in Rs.) of elder brother is
Answer: Option C
Answer: (c)Using Rule 1,Share of elder brother = Rs.x (let)Share of younger brother = Rs.(16820 - x)A = P$(1 + R/100)^T$According to the question,$x(1 + 5/100)^{13} = (16820 - x)(1 + 5/100)^{15}$$x = (16820 - x)(1 + 1/20)^2$$x = (16820 - x)(21/20)^2$$(20/21)^2x = 16820 - x$${400x}/441 + x$ = 16820${400x + 441x}/441$ = 16820841x = 16820 × 441$x = {16820 × 441}/841$ = Rs.8820
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Answer: (c)Using Rule 1,Share of elder brother = Rs.x (let)Share of younger brother = Rs.(16820 - x)A = P$(1 + R/100)^T$According to the question,$x(1 + 5/100)^{13} = (16820 - x)(1 + 5/100)^{15}$$x = (16820 - x)(1 + 1/20)^2$$x = (16820 - x)(21/20)^2$$(20/21)^2x = 16820 - x$${400x}/441 + x$ = 16820${400x + 441x}/441$ = 16820841x = 16820 × 441$x = {16820 × 441}/841$ = Rs.8820
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