Question

The fourth part of a number exeeds the sixth part by 4.Find the number

Answer 1

$\LARGE{ \underline{ \pink{ \sf{Required \: answer:}}}}$

Fourth part of a number means 1/4th of that number. And sixth part means 1/6th of that number. We don't know the number.

Let consider the number be x. The according to question,

• 1/4th of x - 1/6th of x = 4

⇛ $\rm{ \dfrac{x}{4} - \dfrac{x}{6} = 4}$

Taking 12 as LCM in Left hand side,

⇛ $\rm{ \dfrac{3x - 2x}{12} = 4}$

This is equals to,

⇛ $\rm{\dfrac{x}{12} = 4}$

Then for isolating x, let's multiply 12 in the RHS because inverse of division is multiplication:

⇛ $\rm{x = 48}$

And the required number is 48.

Quick check:

• 1/4th of 48 = 12
• 1/6th of 48 = 8

And 1/4th of x - 1/6th of x i.e. 12 - 8 gives 4. This was too mentioned in the question. Hence, proved!

Answer 2

Step-by-step explanation:

$\sf \underline{Given} :$

• The fourth part of a number exeeds the sixth part by 4.

$\sf \underline{To \: Find} :$

• Find the number

$\sf \underline{Solution \: } :$

Let the number be 'x'

$\underline{ \boldsymbol{According \: to \: the \: question.}} :$

$\sf \leadsto \: \frac{x}{4} = \frac{x}{6} + \frac{4}{1}$

Taking L.C.M. of the denominators and solving it, we get.

$\sf \leadsto \: \frac{x}{4} = \frac{x + \cancel{24}}{ \cancel{6} }\\ \\ \sf \leadsto \: 6x = 4x + 96 \\ \\ \sf \leadsto \: 6x - 4x = 96 \\ \\ \sf \leadsto \:2x = 96 \\ \\ \sf \leadsto \: x= \cancel{ \frac{96}{2} } \\ \\ \: \sf \leadsto \:x = 48$

So, the number is 48