Question

6 more than one-fourth of a number is two-fifths of the number.find the number​

Answer 1

Step-by-step explanation:

let the no. be = x

So ATQ

x/4 + 6 = 2x/5

(x +24)/4 = 2x/5

By cross multiplication

5(x + 24) = 4(2x)

5x + 120 = 8x

120 = 3x

40 = x

Answer 2

Answer :-

The number is 40.

Solution :-

Let the number be x

One - fourth of a number = 1/4 * x = x/4

6 more than one - forth of a number = x/4 + 6

Two - fifth of the number = 2/5 * x = 2x/5

Given that

6 more than one - forth of a number = Two - fifth of the number

⇒ x/4 + 6 = 2x/5

Transpose x/4 to RHS

⇒ 6 = 2x/5 - x/4

Taking LCM

⇒ 6 = 2x(4)/5(4) - x(5)/4(5)

⇒ 6 = 8x/20 - 5x/20

⇒ 6 = (8x - 5x)/20

⇒ 6 = 3x/20

Transpose 20 to LHS

⇒ 6(20) = 3x

Transpose 3 to LHS

⇒ 6(20)/3 = x

⇒ 2(20) = x

⇒ 40 = x

⇒ x = 40

Therefore the number is 40.

Verification :-

x/4 + 6 = 2x/5

Substitute x = 40 in the above equation

⇒ 40/4 + 6 = 2(40)/5

⇒ 10 + 6 = 2(8)

⇒ 16 = 16