Shan divides Rs. 1617 between Piyush and Manoj. They invest at 10% CI annually. After 11 and 12 years respectively, both get the same amount. How much did Piyush get?

Correct option is A

Given:
Total amount = Rs. 1617
Piyush and Manoj invest at 10% CI annually.
Piyush withdraws after 11 years, Manoj after 12 years.
Both receive the same final amount.
Formula Used:
​$$A = P(1 + \frac{R}{100})^n$$​​
Solution:
Let P₁ = Amount given to Piyush
Let P₂ = Amount given to Manoj
Condition of equal final amount:
​$$P_1(1.1)^{11} = P_2(1.1)^{12}$$​​
P₁ = 1.1 P₂
P₁ + P₂ = 1617
Substitute the value of P₁
1.1P₂ + P₂ = 1617
2.1P₂ = 1617
P₂ = $$\frac{1617 }{ 2.1}$$​ = 770
Now compute P₁:
P₁ = 1.1 × 770 = 847
Piyush received Rs. 847.