A sum of Rs. 6344 is divided into 3 parts and given on loan at 5% simple interest to A. B and C for 2, 3 and 4 yr, respectively. If this amounts of all three are equal to their respective of loan, then B received a loan of |
A) Rs. 2112
B) Rs. 2128
C) Rs. 2820
D) Rs. 2802
Correct Answer: A
Solution :
Given, sum = Rs. 6344 |
We know that the ratio in which the sum was divided in x parts is given by |
\[=\frac{1}{100+{{R}_{1}}{{T}_{1}}}:\frac{T}{100+{{R}_{2}}{{T}_{2}}}:\frac{1}{100+{{R}_{3}}{{T}_{3}}}\] |
\[=\frac{1}{100+5\times 2}:\frac{1}{100+5\times 3}:\frac{1}{100+5\times 4}\] |
[ \[\because \,\,{{R}_{1}}={{R}_{2}}={{R}_{3}}=5\]% ,\[{{T}_{1}}=2\,yr,\,\,{{T}_{2}}=3yr\,\,\text{and}\,{{T}_{3}}=4\,\,yr\] ] |
\[=\frac{1}{110}:\frac{1}{115}:\frac{1}{120}\] |
\[=\frac{1}{22}:\frac{1}{23}:\frac{1}{24}\] |
\[=23\times 24:22\times 24:22\times 23\] |
\[=552:528=506\] |
Now, B received a loan \[=\frac{528}{1586}\times 6344=\text{Rs}\text{. 2112}\] |
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