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Question

Eight men and 24 women can finish a piece of work in one day while 12 men and 18 women can also finish it in one day. What is the time taken by 24 men and 72 women to finish the work ?

This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is
\(\frac{1}{3}\) of a day

Work Rate Equations Setup

Let \(M\) be the amount of work one man completes in one day, and \(W\) be the amount of work one woman completes in one day. The total work done is the rate multiplied by the time. Since the work is finished in one day in both given scenarios, the total work equals the combined rate of men and women.

From the first statement:

\(8M + 24W = 1 \quad (Equation \, 1)\)

From the second statement:

\(12M + 18W = 1 \quad (Equation \, 2)\)

Solving for Individual Work Rates

We can simplify the equations before solving. Divide Equation 1 by 8:

\(M + 3W = \frac{1}{8} \quad (Equation \, 3)\)

Divide Equation 2 by 6:

\(2M + 3W = \frac{1}{6} \quad (Equation \, 4)\)

Now, subtract Equation 3 from Equation 4 to find the value of \(M\):

\((2M + 3W) - (M + 3W) = \frac{1}{6} - \frac{1}{8}\)

\(M = \frac{4}{24} - \frac{3}{24}\)

\(M = \frac{1}{24}\)

Substitute the value of \(M\) back into Equation 3 to find the value of \(W\):

\(\frac{1}{24} + 3W = \frac{1}{8}\)

\(3W = \frac{1}{8} - \frac{1}{24}\)

\(3W = \frac{3}{24} - \frac{1}{24}\)

\(3W = \frac{2}{24} = \frac{1}{12}\)

\(W = \frac{1}{36}\)

So, one man's work rate is \(\frac{1}{24}\) of the work per day, and one woman's work rate is \(\frac{1}{36}\) of the work per day.

Combined Rate Calculation

We need to find the time taken by 24 men and 72 women. Calculate their combined work rate:

Total Rate = \(24M + 72W\)

\(\text{Total Rate} = 24 \times \left(\frac{1}{24}\right) + 72 \times \left(\frac{1}{36}\right)\)

\(\text{Total Rate} = 1 + 2\)

\(\text{Total Rate} = 3\)

This means 24 men and 72 women together complete 3 units of work per day.

Final Time Determination

To find the time taken to finish 1 unit of work:

\(\text{Time} = \frac{\text{Total Work}}{\text{Total Rate}}\)

\(\text{Time} = \frac{1}{3} \, \text{day}\)

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Similar Questions

  1. A, B, C, D can complete a work in 3, 6, 9, 12 hours respectively. Further, only one person can work at a time in each hour and nobody can work for two consecutive hours. It is not necessary to engage all. What is the minimum number of hours that they will take to finish the work?
  2. 50 men can complete a work in 40 days. They begin the work together but a batch of 5 men left after each period of 10 days. What is the time to complete the work?
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    II. If X and Y work alternately starting with Y, then the piece of work will be finished in less than 5 days.
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Important Questions from Time and work

  1. A person can complete 20% of work in 8 days and another person y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?

  2. P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?

  3. There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?

  4. There is an order of 19000 quantity of a particular product from a customer. The firm produces 1000 quantity of that product per out of which 5% are unfit for sale. In how many days will the order be completed?

  5. Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?

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