Question

$\large\red{\sf{Question}}$
A contractor can complete a certain piece of work, with certain number of men, in 9 days. But 6 of them remained absent from the very first day, so the rest could finish the work in 15 days. How many men were originally employed ?
1-12
2-15
3-18
4-24
​

Answer 1

Answer:

Given :-

• A contractor can complete a certain piece of work, with certain number of men, in 9 days.
• But 6 of them remained absent from the very first day, so the rest could finish the work in 15 days.

To Find :-

• How many men were originally employed.

Solution :-

Let,

$\small \mapsto \bf Men\: were\: originally\: employed =\: x$

According to the question :

$\implies \bf 15 : 9 =\: x : (x - 6)$

$\implies \sf \dfrac{15}{9} =\: \dfrac{x}{(x - 6)}$

By doing cross multiplication we get,

$\implies \sf 9 \times x =\: 15(x - 6)$

$\implies \sf 9x =\: 15x - 90$

$\implies \sf 9x - 15x =\: - 90$

$\implies \sf {\cancel{-}} 6x =\: {\cancel{-}} 90$

$\implies \sf 6x =\: 90$

$\implies \sf x =\: \dfrac{\cancel{90}}{\cancel{6}}$

$\implies \sf x =\: \dfrac{15}{1}$

$\implies \sf\bold{\purple{x =\: 15}}$

Hence, the men were originally employed is :

$\small \dashrightarrow \sf Men\: were\: originally\: employed\: =\: x$

$\small \dashrightarrow \sf\bold{\red{Men\: were\: originally\: employed =\: 15}}$

$\therefore$ The men were originally employed is 15 .

Hence, the correct options is option no (2) 15 .

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Answer 2

Step-by-step explanation:

Let there be x men at the begining less men, more days

∴ 15:9::x:(x−6) ⇒ 15(x−6)=9x

⇒ 6x=90 ⇒ x=15

or

Let the contractor employed 'x' men to complete the task in 9 days.

So, TOTAL WORK = (9x) Mandays

But, 6 out of x men were absent and the remaining completed the work in 15 days.

Thus, TOTAL WORK = 15(x-6) Mandays

So, 9×x=15×(x−6)

=>6×x=90

=>x = 15 Men (Answer)