Question

If 5/6 of a number exceeds its 3/8 by 77. Find the number.​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{Let the number be }x$

       $\text{According to the question:}$

$\implies \dfrac56x = \dfrac38x + 77$

       $\text{Simplifying...}$

$\implies \dfrac{5x}{6} = \dfrac{3x + 616}{8}$

       $\text{Simplifying...}$

$\implies \dfrac{5x}{3} = \dfrac{3x + 616}{4}$

       $\text{Cross-multiplying}$

$\implies 4(5x) = 3(3x + 616)$

       $\text{Simplifying...}$

$\implies 20x = 9x + 5544$

       $\text{Transposing }9x \text{ to L.H.S}$

$\implies 20x - 9x = 5544$

       $\text{Simplifying...}$

$\implies11x = 5544$

       $\text{Transposing }11\text{ to R.H.S}$

$\implies x =\dfrac{5544}{11}$

       $\text{Simplifying...}$

$\implies \boxed{x = 504}$

Answer 2

Step-by-step explanation:

Given that 5/6 of a number exceeds it's 3/8 by 77.

Let's say the number be x.

As per given statement we can write,

→ 5x/6 = 3x/8 + 77

→ 5x/6 - 3x/8 = 77

L.C.M. of 6 and 8 is 24

→ (20x - 9x)/24 = 77

→ 11x/24 = 77

Multiply by 24 on both sides,

→ (11x × 24)/24 = 77(24)

→ 11x = 77(24)

Divide by 11 on both sides,

→ 11x/11 = 77(24)/11

→ x = 7(24)

→ 168

Hence, the value of x is 168.

Method 2)

→ 5x/6 = 3x/8 + 77

→ 5x/6 = (3x + 616)/8

Cross multiply them,

→ 5x(8) = 6(3x + 616)

→ 40x = 18x + 3696

→ 40x - 18x = 3696

→ 22x = 3696

→ x = 3696/22

→ x = 168

Hence, the value of x is 168.