A sum of Rs. 44,200 is divided between John and Smith, 12 years and 14 years old respectively, in such a way that if their portions be invested at 10 percent per annum compound interest, they will receive equal amounts on reaching 16 years of age.

(i) What is the share of each out of Rs. 44,200 ?

(ii) What will each receive, when 16 years old ?

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Solution

Let John's share be x & Smith's share be 44200-x :

John's time =16 -12 = 4 yrs

Smith's time = 16-14 = 2 yrs

According to the question ;

John's amount = Smith's amount

$x (1 + \frac{10}{100})^{4} = (44200 - x) (1 + \frac{10}{100})^{2} x (\frac{11}{10})^{4} = (44200 - x) (\frac{11}{10})^{2} x (\frac{11}{10})^{2} = 44200 - x \frac{121 x}{100} = 44200 - x (\frac{121 x}{100}) + x = 44200 \frac{221 x}{100} = 44200 221 x = 44200 \times 100 221 x = 4420000 x = \frac{4420000}{221} x = 20000$

Hence ,

John's share = x = Rs 20,000

Smith's share = 44 200 - 20 000 = Rs 24200

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