Question

If ¼ of a number is added to ⅓ of that number,the result is 15 greater than half of that number.Find the number.​

Answer 1

GIVEN :-

• 1/4 of a number is added to 1/3 of that number , the result is 15 greater than 1/2 of the number.

TO FIND :-

• The number.

SOLUTION :-

Let the number be 'y'.

So,

♦ 1/4 of y is added to 1/3 of y , result is 15 greater than 1/2 of y.

$\\ \implies \sf \: \dfrac{1}{4} (y) + \dfrac{1}{3} (y) = 15 + \dfrac{1}{2} (y) \\ \\ \implies\sf \: \dfrac{y}{4} + \dfrac{y}{3} = 15 + \dfrac{y}{2} \\ \\ \implies\sf \: \dfrac{y}{4} + \dfrac{y}{3} - \dfrac{y}{2} = 15 \\ \\ \implies\sf \: \dfrac{3(y) + 4(y) - 6(y)}{12} = 15 \\ \\ \implies\sf \: \dfrac{3y + 4y - 6y}{12} = 15 \\ \\ \implies\sf \: \dfrac{y}{12} = 15 \\ \\ \implies\sf \: y = 15 \times 12 \\ \\ \implies\boxed{ \sf \: y =180}$

Hence , the number is 180.

VERIFICATION :-

$\\ \longmapsto\sf \: \dfrac{180}{4} + \dfrac{180}{3} = 15 + \dfrac{180}{2} \\ \\ \longmapsto\sf \: 45 + 60 = 15 + 90 \\ \\ \longmapsto\sf \: 105 = 105 \: \: \: \: \: \: \: \: \: (verified)$