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​



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Answer 1

$\Large{\red{\underline{\underline{\bf{Solution:}}}}}$

• 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.

$⟹4/5th </p><p>$

$=1/3th </p><p>$

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

$\sf{\implies \dfrac{4x}{5}-\dfrac{x + 40}{3} = 24}$

$\sf{\implies \dfrac{12x-5x-200}{15}=24}$

$\sf{\implies \dfrac{7x-200}{15}=24}$

⟹7x−200=360

⟹7x=360+200

⟹7x=560

⟹x=80

$\sf\small\underline\orange{Hence,\:the\: smaller\: number\:(x)=80:-}$

$\sf\small\underline\orange{Hence,\:the\: greater\: number\:(x+40)=120}$

Answer 2

Answer:

Let the required number be 'x', then four fifths of the number = 4/5 x

And three fourths of the number = 3/4x

It is given that 4/5x is greater than3/4 x by 4

⇒ 4/5x- 3/4x = 4

16x- 15x / 20 = 4

= x/20 = 4

x= 80

hence the required number is 80.

Step-by-step explanation:

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