Question

1. One-third of a number is less than the original by 10. Find the number.

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Answer 1

Given :

• One third of a number is less than the original by 10.

To find :

• The original number

~Understanding the concept ::

Here, we have to find the original number if one third of a number is less than the original number by 10. For that firstly, we will assume the original number as x. Then as given in the question, the condition will be 1/3 of x which will be equal to x less than the original number. [Original number = x].

So, condition = 1/3 x = x - 10

Let's do it!

Solution :

Let the original number be x.

$: \implies \boldsymbol{\dfrac{1}{3} \times x = x - 10}$

$: \implies \boldsymbol{\dfrac{1}{3} x = x - 10}$

$: \implies \boldsymbol{\dfrac{1}{3} x - x = - 10}$

$: \implies \boldsymbol{\dfrac{1x - 3x}{3}= - 10}$

$: \implies \boldsymbol{\dfrac{ - 2x}{3}= - 10}$

$: \implies \boldsymbol{- 2x= - 10 \times 3}$

$: \implies \boldsymbol{- 2x= - 30}$

$: \implies \boldsymbol{ \not- 2x= \not- 30}$

$: \implies \boldsymbol{ 2x= 30}$

$: \implies \boldsymbol{x= \dfrac{30}{2} }$

$: \implies \boldsymbol{x= \dfrac{ \cancel{30}}{ \not2} }$

$: \implies \boldsymbol{x= 15 }$

$\leadsto \boldsymbol{the \: value \: of \: x \: = 15}$

$\\ \therefore \underline{ \pmb{the \: original \: number = 15}} \: \: \red \bigstar$

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Let's verify :-

Substitute the value of x in 1/3x = x - 10

Taking Lhs,

⠀⠀⠀⇒ 1/3x

⠀⠀⠀⇒ 1/3 × 15

⠀⠀⠀⇒ 5

Lhs = 5

Taking Rhs,

⠀⠀⠀⇒ x - 10

⠀⠀⠀⇒ 15 - 10

⠀⠀⠀⇒ 5

Rhs = 5

Lhs = Rhs

Hence, verified.