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Simple Interest #12

12. A sum of $₹725$ is lent in the beginning of a year at a certain rate of interest. After $8$ months, a sum of $₹362.50$ more is lent but at the rate twice the former. At the end of the year, $₹33.50$ is earned as interest from both the loans. What was the original rate of interest?
A. $5\%$B. None of these
C. $3.47\%$D. $4.5\%$

Answer: Option C

Explanation:

Solution 1

Suppose $₹725$ is lent out at rate of R% for $1$ year. Then, at the end of 8 months, $₹362.50$ more is lent out at rate of 2R% for the remaining $4$ months($1/3$ year)

Total simple interest $=33.50$
$\Rightarrow \dfrac{725×\text{R}×1}{100}+\dfrac{362.50×\text{2R}×\dfrac{1}{3}}{100}=33.50\\\Rightarrow \dfrac{725\text{R}}{100}+\dfrac{725\text{R}}{100}×\dfrac{1}{3}=33.50\\\Rightarrow \dfrac{725\text{R}}{100}×\dfrac{4}{3}=33.50\\\Rightarrow \dfrac{29\text{R}}{3}=33.50\\\Rightarrow \text{R}=3.47$

Solution 2

$₹725$ is lent out at rate of R% for $1$ year $\cdots(1)$

$₹362.50$ is lent out at rate of 2R% for $4$ months
$\equiv$ $₹362.50$ is lent out at rate of R% for $8$ months
$\equiv$ $₹725$ is lent out at rate of R% for $4$ months $\cdots(2)$

From $(1)$ and $(2),$
Simple interest on $725$ for $1$ year $4$ months at R% $=33.50$

$\text{R}=\dfrac{100×33.5}{725×\dfrac{16}{12}}=\dfrac{33.5}{29×\dfrac{1}{3}}\\=\dfrac{33.5×3}{29}=3.47$

Comments(4)

profileMuruguganesan
2016-05-28 08:43:49 
In this sum of 362.5 more means, 362.5+725=1087.5. Please Explain
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profileJaved Khan
2016-05-29 18:51:39 
After 8 months, total sum lent out is 1087.5 as you said.
But, in this 1087.5, 725 is given at R% and 362.50 at 2R%

Therefore, here the interest is separately calculated as

Interest on 725 for 1 year at R%
+ Interest on 362.50 for 4 months at 2R%
= 33.50
Which gives R=3.46
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profilemiti
2014-10-01 05:24:31 
Shouldn't we calculate interest on Rs 725 for the 4 months?

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profileRaj
2014-10-03 12:59:19 
No. Rs.725 is for one year at R%
Rs.362.50 is for four months at 2R%
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