Name: Cross Multiplication Method: Illustration
Uploaded: 2019-07-19
Duration: 7 min 27 s
Description: This tutorial will show you many examples of solving linear equations in two variables using the cross-multiplication method with a clear step-by-step explan...

Question

Susan invested a certain amount of money in two schemes

A

and

B

, which offer interest at the rate of

8 %

per annum and

9 %

per annum, respectively. She received

₹ 1860

as annual interest. However, had she interchanged the amount of investment in the two schemes, she would have received

₹ 20

more as annual interest. How much money did she invest in each scheme?

Accepted Answer

Let the money invested in scheme $A$ be $₹ x$ and that in scheme $B$ be $₹ y$ .
$Simple interest = \frac{Principal \times Rate \times Time}{100}$
So, interest in scheme $A$ $= \frac{x \times 8 \times 1}{100} = \frac{8 x}{100}$
Interest in scheme $B$ $= \frac{y \times 9 \times 1}{100} = \frac{9 y}{100}$
Total annual interest $= \frac{8 x}{100} + \frac{9 y}{100} = 1860$
$\Rightarrow 8 x + 9 y = 186000 [Multiply both sides by 100] . . . . . (i)$
After inter changing the amounts in the two schemes, the new total annual interest $= \frac{x \times 9 \times 1}{100} + \frac{y \times 8 \times 1}{100} = 20 + 1860$
$\Rightarrow 9 x + 8 y = 188000 [Multiply both the sides by 100] . . . . (i i)$

Now, adding $(i)$ and $(i i)$ , we get:
$17 x + 17 y = 374000 \Rightarrow x + y = 22000 . . . . . (i i i)$
Subtracting $(i)$ from $(i i)$ , we get:
$x - y = 2000 . . . . . (i v)$
Adding $(i i i)$ and $(i v)$ , we get:
$2 x = 24000 \Rightarrow x = 12000$
Putting $x = 12000$ in $(i i i)$ , we get:
$12000 + y = 22000 \Rightarrow y = 10000$
So, the money invested in scheme $A$ is $₹ 12, 000$ and in scheme $B$ is $₹ 10, 000$ .

Important Questions on Pair of Linear Equations in Two Variables

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