Anand has ₹1407 with him. He divides this amount between his two sons, Anil and Ashok, and asks them to invest their respective shares at a compound interest rate of 10% per annum, compounded annually. It is observed that Anil’s investment amounts to the same value after 15 years as Ashok’s investment does after 16 years. How much (in ₹) did Anand give to Ashok?

The correct option is 670.

Step-by-step Explanation:

Let the amount given to Anil be $P_1$ and the amount given to Ashok be $P_2$.

The total amount divided between Anil and Ashok is ₹1407.

$P_1+P_2=1407$

The formula for compound interest amount is given by:

$A=P{\left(1+\frac{r}{100}\right)}^t$

where:

• $P$ = Principal amount
• $r$ = Rate of interest per annum = 10%
• $t$ = Time period in years

According to the question, Anil’s amount after 15 years is equal to Ashok’s amount after 16 years:

$P_1{\left(1+\frac{10}{100}\right)}^{15}=P_2{\left(1+\frac{10}{100}\right)}^{16}$

Simplifying the fraction $1+\frac{10}{100}=\frac{11}{10}$:

$P_1{\left(\frac{11}{10}\right)}^{15}=P_2{\left(\frac{11}{10}\right)}^{16}$

Dividing both sides by ${\left(\frac{11}{10}\right)}^{15}$:

$P_1=P_2\left(\frac{11}{10}\right)$

Rearranging the equation to get the ratio of $P_1$ to $P_2$:

$\frac{P_1}{P_2}=\frac{11}{10}$

This means the ratio of Anil’s share to Ashok’s share is 11 : 10.

The total ratio parts = 11 + 10 = 21 parts.

Now, calculate Ashok’s share ($P_2$):

$P_2=\frac{10}{21}\times 1407$

Since 1407 ÷ 21 = 67:

$P_2=10\times 67=670$

Therefore, Anand gave ₹670 to Ashok.