Question

A man invests a certain sum of money at 6% p.a. simple interest and another sum at 7% p.a. simple interest. His income from interest after 2 years was Rs.354. One fourth of the first sum is equal to one fifth of the second sum. Find sum invested in each.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• Sum invested at 6% per annum be Rs x

and

• Sum invested at 7 % per annum be Rs y.

According to statement

☆ One fourth of the first sum is equal to one fifth of the second sum.

$\rm :\longmapsto\:\dfrac{1}{4} x = \dfrac{1}{5} y$

$\bf\implies \:x = \dfrac{4}{5} y - - - (1)$

We know,

Simple Interest on a certain sum of money P invested at the rate of R % per annum for T years is

$\boxed{ \bf \: Simple \: Interest \: = \: \dfrac{P \times R \times T}{100}}$

Now,

It is given that,

☆ Rs x is invested for 2 years at the eate of 6 % per annum simple interest,

$\rm :\longmapsto\:Simple \: Interest = \dfrac{x \times 6 \times 2}{100}$

$\rm :\longmapsto\:Simple \: Interest = \dfrac{3x}{25}$

Also,

☆ Rs y is invested for 2 years at the rate 7 % per annum simple interest,

$\rm :\longmapsto\:Simple \: Interest = \dfrac{y \times 7 \times 2}{100}$

$\rm :\longmapsto\:Simple \: Interest = \dfrac{7y}{50}$

According to statement

☆ His income from interest after 2 years is Rs 354

$\rm :\longmapsto\:\dfrac{3x}{25} + \dfrac{7y}{50} = 354$

$\rm :\longmapsto\:\dfrac{3}{25} \times\dfrac{4}{5} y +\dfrac{7y}{50} = 354 \: \: \: \{ \: using \: (1) \: \}$

$\rm :\longmapsto\:\dfrac{12}{125} y +\dfrac{7y}{50} = 354 \: \: \:$

$\rm :\longmapsto\:\dfrac{24y + 35y}{250} = 354 \: \: \:$

$\rm :\longmapsto\:\dfrac{59y}{250} = 354 \: \: \:$

$\rm :\longmapsto\:\dfrac{y}{250} = 6 \: \: \:$

$\bf\implies \:y = 1500$

☆ On substituting the value of y in equation (1), we get

$\rm :\longmapsto\:x = \dfrac{4}{5} \times 1500$

$\bf\implies \:x = 1200$

Hence,

• Sum invested at 6% per annum be Rs 1200

and

• Sum invested at 7 % per annum be Rs 1500

Basic Concept Used :-

Basic Concept Used :- Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.