A) Rs. 2750
B) Rs. 2760
C) Rs. 2800
D) Rs. 3050
Correct Answer: B
Solution :
| [b] Let the amount of loan taken by A, B and C respectively be Rs. x, Rs. y and Rs. z. Then, according to the questions, \[x+\frac{x\times 5\times 2}{100}=y+\frac{y\times 5\times 3}{100}=z+\frac{2\times 5\times 4}{100}\] \[\Rightarrow \] \[x+\frac{x}{10}=y+\frac{3y}{20}=z+\frac{z}{5}\]\[\Rightarrow \]\[\frac{11x}{10}=\frac{23y}{20}=\frac{6z}{5}\] \[\Rightarrow \] \[22x=23y=24z=k\] (let) \[\therefore \] \[x=\frac{k}{22},\] \[y=\frac{k}{23}\] and \[z=\frac{5}{24}\] \[\therefore \] \[x+y+z=7930\] \[\Rightarrow \]\[\frac{k}{22}+\frac{k}{23}+\frac{k}{24}=7930\] \[\Rightarrow \]\[\frac{276k+264k+253k}{6072}=7930\] \[\Rightarrow \] \[793k=7930\times 6072\] \[\therefore \] \[k=60720\] Then, the loan taken by \[A=\frac{k}{22}=\frac{60720}{22}=\text{Rs}.\,2760\] |
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