Question

Thirty-five workers build a house in 160 days. How many days will 28 workers take to build the same house, working at the same rate?

Answer 1

Hint: Here, we will first find out the number of days a man takes to build a house. Since more men will take less time to complete the same work, so divide the number of men by the obtained solution to calculate the number of days.

Complete step-by-step solution
It is given that 35 workers can build a house in 160 days.

Now we will find the number of days it will take one man to build a house.

\[
  {\text{No. of days one man take to build house}} = 35 \times 160 \\
   = 5600{\text{ days}} \\
\]

Since when more men will build a house, it will take fewer days than only one man.

We will find the number of days it will take 28 men to build a house, working at the same rate.

\[
  {\text{No. of days 28 men take to build house}} = \dfrac{{5600}}{{28}} \\
   = 200{\text{ days}} \\
\]

Thus, 28 workers take 200 days to build the house, working at the same rate.

Note: In this question, some students mistakenly multiply the value to find the number of days more men will take to build a house, which is wrong. Also, we are supposed to write the values properly to avoid any miscalculation.