Question

$\frac{1}{4}$th of a sum is invested at 3% simple interest, $\frac{1}{3}$rd at 4% and the remainder at 5%. If the total yearly interest is Rs.150, the sum is-

• A. Rs. 4,000
• B. Rs. 3,600
• C. Rs. 3,000
• D. Rs. 5,000

Answer 1

The correct option is B Rs. 3,600

Let sum invested $=Rs.x$

For first part

$P=\frac{1}{4}\times x=\frac{x}{4}$

$R=3$%

$T=1$

$\Rightarrow S.I=\frac{PTR}{100}$

$=\frac{x}{4}\times 1\times \frac{3}{100}$

$=\frac{3x}{400}$

For second part

$P=\frac{1}{3}\times x=\frac{x}{3}$

$R=4$%

$T=1$

$\therefore S.I=\frac{x}{3}\times 1\times \frac{4}{100}$

$=\frac{x}{75}$

For third part

$P=x-(\frac{x}{4}+\frac{x}{3})$

$=x-\left(\frac{7x}{12}\right)$

$=\frac{5x}{12}$

$R=5$%

$T=1$

$S.I=\frac{PTR}{100}$

$\Rightarrow S.I=\frac{5x}{12}\times 1\times \frac{5}{100}$

$=\frac{x}{48}$

ATP,

$\frac{3x}{400}+\frac{x}{75}+\frac{x}{48}=150$

$\frac{9x+16x+25x}{1200}=150$

$\Rightarrow 50x=150\times 1200$

$\Rightarrow x=\frac{150\times 1200}{50}$

$=3,600$

$\therefore$ The sum is $Rs$ $3600$.