Name: Fractions Using Cross Multiplication
Uploaded: 2019-07-19
Duration: 3 min 47 s
Description: Learn how to compare two fractions with each other by using the fairly straightforward method of cross-multiplication. Master this concept now by watching th...

Question

A man invested

₹ 36000

, a part of it at

12 %

and the rest at

15 %

per annum simple interest. If he received a total annual interest of

₹ 4890

, how much did he invest at each rate?

Accepted Answer

Let the sum invested at $12 %$ and $15 %$ per annum simple interest be $₹ x$ and $₹ y$ , respectively.

So, we have $₹ x + ₹ y = ₹ 36000 \Rightarrow x + y = 36000 \Rightarrow y = 36000 - x$ -----(i)

Again, by the condition given in the question, we get, $\frac{x \times 12 \times 1}{100} + \frac{y \times 15 \times 1}{100} = 4890$

[The simple interest $= \frac{P \times R \times T}{100}$ , where $P =$ the principal amount, $R =$ rate of interest and $T =$ time]

$\Rightarrow \frac{3 x}{25} + \frac{3 y}{20} = 4890$

$\Rightarrow \frac{3 x}{25} + \frac{3 \times (36000 - x)}{20} = 4890$

$\Rightarrow \frac{3 x}{25} \times 100 + \frac{108000 - 3 x}{20} \times 100 = 4890 \times 100$

$\Rightarrow 12 x + 5 (108000 - 3 x) = 489000$

$\Rightarrow 12 x + 540000 - 15 x = 489000$

$\Rightarrow - 3 x = 489000 - 540000$

$\Rightarrow - 3 x = - 51000$

$\Rightarrow x = \frac{- 51000}{- 3} = 17000$

From (i), we get, $y = 36000 - x = 36000 - 17000 = 19000$

Therefore, the required sum invested at $12 %$ is $₹ 17000$ and that invested at $15 %$ is $₹ 19000$ .

A man invested $₹ 36000$ , a part of it at $12 %$ and the rest at $15 %$ per annum simple interest. If he received a total annual interest of $₹ 4890$ , how much did he invest at each rate?

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

A man invested ₹36000, a part of it at 12% and the rest at 15% per annum simple interest. If he received a total annual interest of ₹4890, how much did he invest at each rate?

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

A man invested $₹ 36000$ , a part of it at $12 %$ and the rest at $15 %$ per annum simple interest. If he received a total annual interest of $₹ 4890$ , how much did he invest at each rate?