Question

A part of Rs. 1500 was lent at 10% p.a. and the rest at 7% p.a. simple interest. The total interest earned in three years was Rs. 936. The sum lent at 10% was?
(A) Rs. 900
(B) Rs. 800
(C) Rs. 700
(D) Rs. 600

Answer 1

Hint: Assume that Rs. x is lent at 10% for 3 years. Now, calculate the interest using the formula, \[\text{Simple Interest=}\dfrac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}\] . Since the sum is Rs. 1500 and x is lent at the rate of 10% for 3 years. So, the remaining sum Rs. \[\left( 1500-x \right)\] is lent at the rate of 7% for 3 years. Now, calculate the interest using the formula, \[\text{Simple Interest=}\dfrac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}\] . It is given that the total interest is Rs. 396. Now, solve it further and get the value of x.

Complete step-by-step answer:
According to the question, it is given that A part of Rs. 1500 was lent at 10% p.a. and the rest at 7% p.a. simple interest. The total interest earned in three years was Rs. 936. We have to find the sum that was lent at 10%.
The total interest earned in three years = Rs. 396 …………………………….(1)
Let us assume that the sum lent on 10% is Rs. x.
Since some part of the sum Rs. 1500 is lent at 10% while the remaining part is lent at 7%.
The total sum = Rs. 1500 …………………………………(2)
The part of the sum lent at the rate of 10% = Rs. x …………………………(3)
The part of the sum lent at 7% = Rs. \[\left( 1500-x \right)\] …………………………(4)
It is given that the sum is lent for 3 years.
We know the formula, \[\text{Simple Interest=}\dfrac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}\] …………………………………(5)
For the sum of Rs. x which is lent at the rate of 10% for 3 years, we have
Principal = x ………………………….(6)
Time = 3 years ………………………………(7)
Rate = 10% ………………………………………(8)
From equation (5), equation (6), equation (7), and equation (8), we get
The interest on the sum lent at the rate of 10% for 3 years = \[\dfrac{x\times 10\times 3}{100}=\dfrac{3x}{10}\] ………………………………….(9)
For the sum of Rs. \[\left( 1500-x \right)\] which is lent at the rate of 7% for 3 years, we have
Principal = Rs. \[\left( 1500-x \right)\] ………………………….(10)
Time = 3 years ………………………………(11)
Rate = 7% ………………………………………(12)
From equation (5), equation (10), equation (11), and equation (12), we get
The interest on the sum lent at the rate of 7% for 3 years = \[\dfrac{\left( 1500-x \right)\times 7\times 3}{100}=\dfrac{21\left( 1500-x \right)}{100}\] ………………………………….(13)
From equation (9) and equation (13), we have the interest on the sum of Rs. x and Rs. \[\left( 1500-x \right)\] in three years.
The total interest earned in three years = Rs. \[\dfrac{3x}{10}+\dfrac{21\left( 1500-x \right)}{100}\] ………………………….(14)
From equation (1), we also have the total interest earned in three years.
On comparing equation (1) and equation (14), we get
\[\begin{align}
  & \Rightarrow \dfrac{3x}{10}+\dfrac{21\left( 1500-x \right)}{100}=396 \\
 & \Rightarrow 30x+31500-21x=39600 \\
 & \Rightarrow 30x-21x=39600-31500 \\
 & \Rightarrow 9x=8100 \\
 & \Rightarrow x=\dfrac{8100}{9} \\
 & \Rightarrow x=900 \\
\end{align}\]
The value of x is Rs. 900.
Hence, Rs. 900 is the sum that was lent at 10% for 3 years.

Note: The best way to solve this type of question is to assume a part of the sum as x and then get the remaining part of the sum. Now, use the formula, \[\text{Simple Interest=}\dfrac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}\] and calculate the interest for both parts of the sum.