Question : A sum of Rs. 3,500 is lent out at simple interest in two parts. One part at the annual rate of 7% and another part at the annual rate of 5%. If the total annual interest is Rs. 210, then what is the sum lent out at the rate of 7%?
Option 1: Rs. 1,750
Option 2: Rs. 2,000
Option 3: Rs. 1,500
Option 4: Rs. 2,250
Correct Answer: Rs. 1,750
Solution :
Given: A sum of Rs. 3,500 is lent out at simple interest in two parts.
Use the formula, $SI=\frac{P\times R\times T}{100}$ where $SI$, $P$, $R$, and $T$ are the simple interest, principal, rate, and time.
According to the question,
⇒ $\frac{P\times 7\times 1}{100}+\frac{(3500-P)\times 5\times 1}{100}=210$
⇒ $\frac{7P}{100}+\frac{(3500-P)\times5}{100}=210$
⇒ $7P+17500-5P=21000$
⇒ $2P=3500$
⇒ $P= 1,750$
Hence, the correct answer is Rs. 1,750.
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