A) Rs. 1400
B) Rs. 1500
C) Rs. 1550
D) Rs. 1600
Correct Answer: B
$ \therefore $ $ ( x+\frac{x\times 3\times 5}{100} )+( x+\frac{x\times 2\times 5}{100} ) $ $ +( x+\frac{x\times 1\times 5}{100} )+x=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}=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{rt(t-1)}{2}} $
Here, $ A=6450 $
$ \Rightarrow $ $ t=4yr $
$ \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=Rs\text{. 1500} $
BETA
