Question

76 ladies can complete a job in 33 days. Due to some reason, some ladies did not join the work and therefore, it was completed in 44 days. The number of ladies who did not report for the work is
(a) 17
(b) 18
(c) 19
(d) 20

Answer 1

Hint:
Here, we need to find the number of ladies who did not report for the work. Let the number of ladies who did not report for the work be \[x\]. Using the given information, you need to find the work done by 1 lady in 1 day. You need to subtract the number of ladies and number of ladies who did not report to find the number of ladies who reported for work. Then, using this, find the work done by 1 lady in 1 day. Finally, you need to equate the two equations, and simplify to find the value of \[x\], and hence the number of ladies who did not report for the work.

Complete step by step solution:
Let the number of ladies who did not report for the work be \[x\].
Now, we know that 76 ladies could complete the job in 33 days.
Dividing by 33, we get
Amount of work done by 76 ladies in 1 day \[ = \dfrac{1}{{33}}\]
Dividing the expression by 76, we get
Amount of work done by 1 lady in 1 day \[ = \dfrac{1}{{33 \times 76}} \ldots \ldots \ldots \left( 1 \right)\]
Now, we know that \[x\] ladies did not report for the work.
We can find the number of ladies who reported to work by subtracting the number of ladies who did not report from the number of ladies who were expected to report.
Therefore, we get
Number of ladies who reported \[ = 76 - x\]
We know that the \[76 - x\] ladies completed the work in 44 days.
Dividing by 44, we get
Amount of work done by \[76 - x\] ladies in 1 day \[ = \dfrac{1}{{44}}\]
Dividing the expression by \[76 - x\], we get
Amount of work done by 1 lady in 1 day \[ = \dfrac{1}{{44\left( {76 - x} \right)}} \ldots \ldots \ldots \left( 2 \right)\]
Now, comparing equation \[\left( 1 \right)\] and equation \[\left( 2 \right)\], we can observe that
\[\dfrac{1}{{33 \times 76}} = \dfrac{1}{{44\left( {76 - x} \right)}}\]
We will simplify this equation to get the value of \[x\].
Rewriting the equation, we get
\[ \Rightarrow 33 \times 76 = 44\left( {76 - x} \right)\]
Multiplying the terms in the equation, we get
\[ \Rightarrow 2508 = 3344 - 44x\]
Rewriting the equation and subtracting the terms, we get
  $ \Rightarrow 44x = 3344 - 2508 \\
   \Rightarrow 44x = 836 $
Dividing both sides of the equation by 44, we get
  $ \Rightarrow \dfrac{{44x}}{{44}} = \dfrac{{836}}{{44}} \\
  \therefore x = 19 $

Therefore, the number of ladies who did not report for work is 19. The correct option is option (c).

Note:
Here, the work done when completed is taken as 1. This is why we divided 1 by 33 to get the amount of work done by 76 ladies in 1 day. Similarly, we divided 1 by 44 to get the amount of work done by \[76 - x\] ladies in 1 day.