Question

if the sum of two number is 63 and their difference is 13.then what is the product of those number.?

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Answer 1

let the two numbers be x and the other is y

x+y=63......(1)

x-y= 13......(2)

2x= 76

x=38

x+y=63 ( from 1)

38+y=63

y=63-38

y=25

the product of those number =xy =38x 25 = 950

the product of those number is 950.

Answer 2

Given :–

• Sum of two numbers = 63.
• Difference of two numbers = 13.

To Find :–

• Product of those numbers.

Solution :–

Let,

The first number be x.

And the second number be y.

So,

According to the question,

• x + y = 63 –––––––(1)
• x – y = 13 –––––––(2)

First, we have to find the value of y.

So,

From equation (2),

⟹ x – y = 13

• x = 13 + y

Substitute this value in equation (1),

• x + y = 63

⟹ 13 + y + y = 63

⟹ 13 + 2y = 63

⟹ 2y = 63 – 13

⟹ 2y = 50

⟹ y = $\dfrac{\cancel{50}}{\cancel{2}}$

Cut the denominator and the numerator by 2, we obtain

⟹ y = 25

• y = 25

Now, put the value of y in equation (2),

• x – y = 13

⟹ x – 25 = 13

⟹ x = 13 + 25

⟹ x = 38

Hence,

• First number is 38.
• Second number is 25.

Check :–

1. Sum of two numbers is 63.

⟹ x + y = 63

• x = 38
• y = 25

⟹ 38 + 25 = 63

⟹ 63 = 63

2. Difference of two numbers is 13.

⟹ x – y = 13

• x = 38
• y = 25

⟹ 38 – 25 = 13

⟹ 13 = 13

In both 1 and 2 checking the L.H.S. and the R.H.S. is equal.

So, the answer is correct.

Now, we need to find the products of both numbers.

So,

⟹ x × y

• x = 38
• y = 25

⟹ 38 × 25

⟹ 950

Hence,

The product of those numbers is 950.