Correct Answer - Option 3 : 2400
Given:
A man invested his capital in the ratio of 4 ∶ 3 ∶ 5
first part at 7%, second at 8% and third at 10 % simple interest
Annual income = Rs. 204
Concept used:
S.I. = (P × T × R)/100
Where,
S.I. → Simple interest
P → Principal
T → Time
R → Rate
Calculations:
Let the amount invested at 7%, 8%, and 10% be 4x, 3x and 5x respectively.
S.I. = (P × T × R)/100
\( \Rightarrow \frac{{4{\rm{x\;}} \times {\rm{\;}}1{\rm{\;}} \times {\rm{\;}}7}}{{100}} + \frac{{3{\rm{x\;}} \times {\rm{\;}}1{\rm{\;}} \times {\rm{\;}}8}}{{100}} + \frac{{5{\rm{x\;}} \times {\rm{\;}}1\; \times {\rm{\;}}10}}{{100}}{\rm{}} = 204\)
⇒ 28x + 24x + 50x = 20400
⇒ 102x = 20400
⇒ x = 200
So, the total capital = 4x + 3x + 5x = 12x
⇒ 12 × 200 = Rs. 2400
∴ The total capital is Rs. 2400
