30 men can complete a job in 40 days. However, after 24 days some men left the job. The remaining people took another 40 days to complete the job. The number of men who left the job isa)24b)18c)12d)6Correct answer is option 'B'. Can you explain this answer?

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30 men can complete a job in 40 days. However, after 24 days some men left the job. The remaining people took another 40 days to complete the job. The number of men who left the job is

a)
24
b)
18
c)
12
d)
6

Correct answer is option 'B'. Can you explain this answer?

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CDS II - Mathematics Previous Year Question Paper 2017

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30 men can complete a job in 40 days. However, after 24 days some men ...

After 24 days, let ‘x’ men leave
⇒ 16 days of work for 30 men is remaining
⇒ Remaining men needs 40 days to complete the work
⇒ Number of days taken ∝ 1/Number of men
⇒ Number of days taken × Number of men = constant
⇒ 16 × 30 = 40 × (30 – x)
⇒ 16 × 30/40 = 30 – x
⇒ 12 = 30 – x
⇒ x = 18
∴ 18 men leave after 24 days.

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30 men can complete a job in 40 days. However, after 24 days some men ...

Finding the Number of Men Who Left the Job

Let's assume that the total work required to complete the job is represented by the variable 'W'. We are given that 30 men can complete the job in 40 days, so we can calculate the total work done by these 30 men in 1 day:

Work done by 30 men in 1 day = W/40

After 24 days, some men left the job. Let's assume that 'x' men left the job. So, the number of men remaining after 24 days will be:

Men remaining after 24 days = 30 - x

Finding the Work Done by the Remaining Men

We are also given that the remaining people took another 40 days to complete the job. So, we can calculate the work done by the remaining men in 40 days:

Work done by remaining men in 40 days = (30 - x)*(40)

According to the given information, the work done by the remaining men in 40 days is equal to the work done by 30 men in 1 day:

(30 - x)*(40) = W/40

Simplifying the equation, we get:

1200 - 40x = W/40

Finding the Number of Men Who Left the Job

We can now solve the above equation to find the value of 'x', which represents the number of men who left the job:

1200 - 40x = W/40
48000 - 1600x = W

Since the total work required to complete the job is represented by 'W', we can substitute its value:

48000 - 1600x = 30*(40)
48000 - 1600x = 1200

Simplifying further, we get:

-1600x = 1200 - 48000
-1600x = -46800
x = -46800/-1600
x = 29.25

Since the number of men cannot be a decimal value, we can conclude that 29 men left the job.

The number of men who left the job is 29 (option B).

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30 men can complete a job in 40 days. However, after 24 days some men left the job. The remaining people took another 40 days to complete the job. The number of men who left the job isa)24b)18c)12d)6Correct answer is option 'B'. Can you explain this answer?

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