Question

2. यदि दो संख्याओं का योग 97 है तथा अन्तर 37 है तो उनका गुणनफल क्या होगा?
(a)2378
(b) 8040
(c) 2010 (d) 1736​

Answer 1

Given:

यदि दो संख्याओं का योग 97 है तथा अन्तर 37 है तो उनका गुणनफल क्या होगा?

If the sum of two numbers is 97 and the difference is 37, what will be their product?

To find:

The product of the two numbers

Solution:

Let "x" and "y" be the two numbers.

The sum of two numbers is 97, so the equation will be:

$x + y = 97 \:.\: .\: . \:(1)$

The difference between the two numbers is 37, so the equation will be:

$x - y = 37 \:.\: .\: . \:(2)$

On adding equations (1) and (2), we get

x + y = 97

x - y = 37

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2x = 134

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∴ $\bold{x } = \frac{134}{2} = \bold{67}$

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

$x + y = 97$

$\implies 67 + y = 97$

$\implies y = 97 - 67$

$\implies \bold{y = 30}$

Now,

The product of the two numbers is,

= xy

= $67 \times 30$

= $\bold{2010}$ ← option (c)

Thus, the product of the two numbers is → 2010.

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