Question : A sum of Rs. 4,000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352, the sum lent at 8% is:
Option 1: Rs. 2,900
Option 2: Rs. 2,200
Option 3: Rs. 2,400
Option 4: Rs. 3,100
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Correct Answer: Rs. 2,400
Solution :
Let the sum lent at 8% as $x$ and the sum lent at 10% as $(4000 - x)$.
Simple interest (S.I.)=$\frac{\text{Principal×Rate×Time}}{100}$
Where $S.I.$ is the simple interest, $P$ is the principal amount, $R$ is the rate of interest and $T$ is the time in years.
The total interest from both parties is Rs. 352.
$⇒0.08x + 0.10(4000 - x) = 352$
$⇒0.08x + 400 - 0.10x = 352$
$⇒-0.02x + 400 = 352$
$⇒-0.02x = -48$
$⇒x = \frac{-48}{-0.02} = 2400$
Hence, the correct answer is Rs. 2,400.
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