Question

Divide Rs. 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is

• A. Rs. 759
• B. Rs. 792
• C. Rs. 818
• D. Rs. 828

Answer 1

The correct option is D Rs. 828

Let the parts be x, y and z
Rate of interest=5%
x + interest on x for 2 years = y + interest on y for 3 years = z + interest on z for 4 years
$(x+\frac{x\times 5\times 2}{100})=(y+\frac{y\times 5\times 3}{100})=(z+\frac{z\times 5\times 4}{100})$
$=(x+\frac{x}{10})+(y+\frac{3y}{20})+(z+\frac{z}{5})$
$=\frac{11x}{10}=\frac{23y}{20}=\frac{6z}{5}=K$
Then $x=\frac{10K}{11},y=\frac{20K}{23},z=\frac{5K}{6}$
According to the question $x+y+z=2379$
so$\frac{10K}{11}+\frac{20K}{23}+\frac{5K}{6}=2379$
$1380K+1320K+1265K=2379\times 11\times 23\times 6$
$3965K=2379\times 11\times 23\times 6$
$K=\frac{2379\times 11\times 23\times 6}{3965}$
So first part$=x=\frac{10K}{11}=\frac{10}{11}\times \frac{2379\times 11\times 23\times 6}{3965}$
$x=\frac{2379\times 10\times 23\times 6}{3965}$
$x=828$