| What annual payment will discharge a debt of Rs. 6450 due in 4 yr at 5% per annum simple interest? [SSC (CGL) 2010, 2005] |
A) Rs. 1400
B) Rs. 1500
C) Rs. 1550
D) Rs. 1600
Correct Answer: B
Solution :
| Let the annual instalment be Rs. x. |
| \[\therefore \]\[\left( x+\frac{x\times 3\times 5}{100} \right)+\left( x+\frac{x\times 2\times 5}{100} \right)\] |
| \[+\left( x+\frac{x\times 1\times 5}{100} \right)+x=\text{Rs}\text{. 6450}\] |
| \[\Rightarrow \]\[\frac{115x}{100}+\frac{110x}{100}+\frac{105x}{100}+x=6450\] |
| \[\Rightarrow \]\[115x+110x+105x+100x=6450\times 100\] |
| \[\Rightarrow \] \[430x=6450\times 100\] |
| \[\therefore \] \[x=\frac{6450\times 100}{430}=\text{Rs}\text{. 1500}\] |
| Alternate Method |
| The annual payment that will discharge a debt of Rs. A due in 4 yr at the rate of interest r% per annum, is |
| \[\frac{100A}{100t+\frac{r\,\,t\,\,(t-1)}{2}}\] |
| Here, \[A=6450\]\[\Rightarrow \]\[t=4\,\,yr\]\[\Rightarrow \]\[r=5\]% |
| \[=\frac{100\times 6450}{100\times 4+\frac{5\times 4\,\,(4-1)}{2}}\] |
| \[=\frac{100\times 6450}{400+30}=\frac{100\times 6450}{430}\] |
| \[\therefore \] \[A=\text{Rs}\text{. 1500}\] |
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