Question

1. Find a number such that if 5,15 and 35
are added to it, the product of the first and
third results may be equal to the square of
the second
(a) 10 (b) 7 (c) 6 (d) 5​

Answer 1

Answer :

option (d) 5

Step-by-step explanation :

Given :

If 5,15 and 35  are added to a number, the product of the first and  third results may be equal to the square of  the second result.

To find :

the number

Solution :

Let the number be "x"

If 5 is added to it, the result is (x + 5)

If 15 is added to it, the result is (x + 15)

If 35 is added to it, the result is (x + 35)

So,

the first result = (x + 5)

the second result = (x + 15)

the third result = (x + 35)

As given,

 (x + 5) (x + 35) = (x + 15)²

(x + 5) (x + 35) = (x + 15) (x + 15)

x(x + 35) + 5(x + 35) = x(x + 15) + 15(x + 15)

x² + 35x + 5x + 175 = x² + 15x + 15x + 225

x² + 40x + 175 = x² + 30x + 225

 40x + 175 = 30x + 225

 40x - 30x = 225 - 175

  10x = 50

    x = 50/10

    x = 5

∴ The number is 5

Verification :

If 5 is added to it, the result is (5 + 5) = 10

If 15 is added to it, the result is (5 + 15) = 20

If 35 is added to it, the result is (5 + 35) = 40

Condition : the product of the first and  third results may be equal to the square of  the second

 10 × 40 = 20²

  400 = 20 × 20

  400 = 400

 LHS = RHS

Hence verified!