Question

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

Answer 1

Answer:

The number is 40

Step-by-step explanation:

Let the number be 'a'

• one - fourth of a number

  $\sf = \dfrac{1}{4} \times a \\\\\\ = \dfrac{a}{4}$

• 6 more than one - fourth of the number

  $\sf = \dfrac{a}{4}+6$

• two - fifth of the number

  $\sf = \dfrac{2}{5} \times a \\\\\\ =\dfrac{2a}{5}$

6 more than one - fourth of a number = two - fifth of the number

         $\sf \dfrac{a}{4}+6=\dfrac{2a}{5} \\\\\\ 6=\dfrac{2a}{5}-\dfrac{a}{4} \\\\\\ 6= \dfrac{2a \times 4}{5 \times 4} -\dfrac{a \times 5}{4 \times 5} \\\\\\ 6=\dfrac{8a}{20} -\dfrac{5a}{20} \\\\\\ 6=\dfrac{8a-5a}{20} \\\\ 6=\dfrac{3a}{20}\\\\ 3a= 6 \times 20 \\\\ 3a=120 \\\\ a=120/3 \\\\ a=40$

The number is 40.

Verification :

$\sf 6+\dfrac{40}{4} = \dfrac{2 \times 40}{5} \\\\ 6 + 10= 2 \times 8 \\\\ 16=16 \\\\ LHS=RHS$

Hence verified!

Answer 2

Answer:

See the attachment........