Question

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

Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

${ \bf{ \underbrace{ \purple{Required \: Answer :}}}}$

Given :

• 6 more than one fourth of a number is two fifths of the number.

To find :

• The number ?

Solution :

✒ Let the number be 'x'

☞ One – fourth of the number = x/4

☞ Two-fifth of the number = 2x/5

◊ According to the Question :

$➙ \: { \sf{6 + \frac{1}{4} x = \frac{2}{5} x}}$

$➙ \: { \sf{6 + \frac{x}{4} = \frac{2x}{5} }}$

〖 Multiplying each term by 20 because L.C.M of 5, 4 and 1 is 20 〗

$➙ \: { \sf{120 + 5x = 8x}}$

$➙ \: { \sf{120 = 8x - 5x}}$

$➙ \: { \sf{120 = 3x}}$

$➙ \: { \sf{ \cancel\frac{120}{3} = x}}$

$➙ \: { \boxed{ \sf{ \green{40 = x}}}}$

◙ Hence, the required number is 40.

________________________