Divide ₹ 21,866 into two parts such that the amount of the first part for 3 years and amount of the second part for 5 years are equal at the same rate of 5% compound interest.
Let the first part be ₹ x and the second part be ₹ (21866 – x) . We have
Amount after 3 years = x(1 + 5\over 100)³ = x(105\over 100)³
Amount after 5 years = (21866 – x)(1 + 5\over 100)5
= (21866 – x)(105\over 100)5
Since these amounts are equal,
x(105\over 100)³ = (21866 – x)(105\over 100)5
x = (21866 – x)(105\over 100)²
⇒ x = (21866 – x)(11025\over 10000)
⇒ 10000x = 21866 × 11025 – 11025 x
⇒ 10000x + 11025 x = 21866 × 11025
⇒ 10000x + 11025 x = 21866 × 11025
⇒ 21025 x = 21866 × 11025
⇒ x = 21866 × 11025 \over 21025
⇒ x = 21866 × 11025 \over 21025 = ₹ 11466
Thus, the first part is ₹ 11,466 and the second part is ₹ 10,400.
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