Math, asked by keyur512, 1 year ago

One-sixth of a number is 16 less than the one-fourth of the number. Find the number

Answers

Answered by BrainlyRacer
12

Solution

========================

Let the number is 'x'

So,

One-sixth of a number =  \bold{\dfrac{x}{6}}

One - fourth of number =  \bold{\dfrac{x}{4}}

==========================

⋆ Given that :

One-sixth of a number is 16

less than one fourth of the number.

===========================

⋆ To find :

We have to find that number

which we have taken as 'x'.

============================

★ Now we are going to solve

   that equation.

According to the question

\implies\dfrac{x}{6}=\dfrac{x}{4}-16\\\\\\\implies\dfrac{x}{6}-\dfrac{x}{4}=-16\\\\\\\implies\dfrac{2x-3x}{12}=-16\\\\\\\implies\dfrac{-x}{12}=-16\:('-'\:and\:'-'\:will\:cancelled)\\\\\\\implies x=16\times12\\\\\\\implies\boxed{x=192}

================================

★ Now we are going to verify

   our answer

To verify our answer we have

to put '192' at the place of 'x'

==============================

★ Lets do it

\implies\dfrac{192}{6}=\dfrac{192}{4}-16\\\\\\\implies\dfrac{192}{6}-\dfrac{192}{4}=-16\\\\\\\implies\dfrac{384-576}{12}=-16\\\\\\\implies\dfrac{-192}{12}=-16\:('-'\:and\:'-'\:will\:cancelled)\\\\\\\implies 192=16\times12\\\\\\\implies\boxed{192=192}

===============================

★Here, L.H.S = R.H.S

  Hence, it is verified


deepsen640: great answer
Answered by Anonymous
12

\bf{\large{\underline{\underline{Answer:-}}}}

Required number is 192

\bf{\large{\underline{\underline{Explanation:-}}}}

Given :- One - Sixth of a number is 16 less than One - fourth of a number.

To find :- Required number

Solution :-

Let the number be x

One - Sixth of a number = 1/6 * x = x/5

One - Fourth of a number = 1/4 * x = x/4

16 less than one - Fourth of a number = x/4 - 16

Given that One - Sixth of a number is 16 less than One - fourth of a number.

Accordind to the question :-

 \dfrac{x}{6} =  \dfrac{x}{4} - 16

 \dfrac{x}{6} + 16 =  \dfrac{x}{4}

16 =  \dfrac{x}{4} -  \dfrac{x}{6}

Least Common Factor of 4 and 6 is 12

16 =  \dfrac{x(3)}{4(3)} -  \dfrac{x(2)}{6(2)}

16 =  \dfrac{3x}{12} -  \dfrac{2x}{12}

16 =  \dfrac{x}{12}

16 \times 12 = x

x = 192

\bf{\large{\underline{\underline{Verification:-}}}}

We got the required number as 192. To check whether it us correct or not substitute x = 192 in the equation that is formed to solve.

 \dfrac{192}{6} =  \dfrac{192}{4} - 16

 \dfrac{192 \div 6}{6 \div 6} =  \dfrac{192 \div 4}{4 \div 4} - 16

32 = 48 - 16

32 = 32

Here Left Hand Side = Right Hand Side

So, Required number is 192


deepsen640: very nice explanation
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