Question

A number is divided into two parts so that the difference of the parts is 40. If four-fifth of the smaller part exceeds one-third of the greater part by 24. Find the number​

Answer 1

Step-by-step explanation:

$\tt\large\underline\purple{Let:-}Let:−$

$</p><p>\sf{The\: smaller\:part=x}</p><p>$

$\sf{The\: greater\:part=x + 40}$

$\tt\large\underline\purple{To\:Find:-}$

$</p><p>\sf{The\:smaller\: number=?}$

$\sf{The\: greater\: number=?}$

$\tt\large\underline\purple{Solution:-}$

To calculate the required number at first we have to set up equation. Before calculating we have to assume the smaller part be x and the greater part = ? here we will solve the greater part. As given in the question that the difference between two parts = 40 , so set equation here like this . The greater part - smaller part = 40 => greater part - x = 40 so, the greater part = x + 40.

\tt\large\underline{As\:per\:the\: question:-}Asperthequestion:−

\tt\small{\implies 4/5th\:_{(smaller\:no)} = 1/3th\:_{(greater\:no)}+24}⟹4/5th(smallerno)=1/3th(greaterno)+24

\sf{\implies \dfrac{4x}{5}=\dfrac{x + 40}{3} + 24}⟹54x=3x+40+24

\sf{\implies \dfrac{4x}{5}-\dfrac{x + 40}{3} = 24}⟹54x−3x+40=24

\sf{\implies \dfrac{12x-5x-200}{15}=24}⟹1512x−5x−200=24

\sf{\implies \dfrac{7x-200}{15}=24}⟹157x−200=24

\sf{\implies 7x - 200 = 360}⟹7x−200=360

\sf{\implies 7x = 360 + 200}⟹7x=360+200

\sf{\implies 7x = 560}⟹7x=560

\sf{\implies x = 80}⟹x=80

\sf\small\underline\pink{Hence,\:the\: smaller\: number\:(x)=80:-}Hence,thesmallernumber(x)=80:−

\sf\small\underline\pink{Hence,\:the\: greater\: number\:(x+40)=120:-}Hence,thegreaternumber(x+40)=120:−