Question

Mr. Shaikh invested Rs.4,00,000 in the glass industry. After $2$ years he received $Rs.5,20,000$ from the industry. Putting aside the original investment, he invested his gains in a fixed deposit and in shares in the ratio $3:2$ . How much amount did he invest originally in each of the schemes?

Answer 1

Hint: In Mathematics, a ratio is nothing but the quantitative relation between two numbers that shows how one number is compared with another. The relation can be between more than two numbers with a condition that they must have the same unit. Generally, we use the symbol”:” to denote a ratio. The concept ratio plays a vital role in real-life applications too.

Complete step-by-step solution:
From the given information, we can understand that Mr. Shaikh invested $Rs.4,00,000$ in the glass industry and after $2$ years he received $Rs.5,20,000$ from the industry
The gain that Mr. Shaikh at the end of two years in glass industry
=$Rs.5,20,000-Rs.4,00,000$
$ = Rs.1,20,000$ ….$\left( 1 \right)$
It is given that he invested his gains in a fixed deposit and shares in the ratio $3:2$.
Let the amount invested in the first share be $3x$ .
Similarly, let the amount invested in the second share be $2x$.
Now, we shall compare the gain obtained in the equation $\left( 1 \right)$ with the above gains.
That is $3x + 2x = Rs.1,20,000$
$ \Rightarrow 5x = 120000$
$ \Rightarrow x = \dfrac{{120000}}{5}$
$ \Rightarrow x = 24000$
Now, we need to substitute the value of $x$ our assumption.
The amount invested in the fixed deposit $ = 3x$
$ = 3 \times 24000$
$ = Rs.72000$
Similarly, the amount invested in shares $ = 2x$
$ = 2 \times 24000$
$ = Rs.48000$
Therefore, Mr. Shaikh's investment of $Rs.72000$ in the fixed deposit and $Rs.48000$ shares is the required answer.

Note: A ratio is a quantitative expression that is used to compare the size of two things or more than two things. Sometimes, the relation can be between more than two numbers with a condition that they must have the same unit. Generally, we use the symbol”:” to denote a ratio.