Question

Rahul can finish one-fifth of his homework in one hour. Neha can finish three-sevenths of her homework in one hour thirty minutes and Riya can finish three fourths of her homework in three hours thirty minutes. If all of them can start their homework at $ 12.00p.m $ . And can go to play as soon as they all finish their homework, when can they start to play if they take a break at $ 3.30p.m $ For thirty minutes?

Answer 1

Hint: In order to find the play time for the kids, we need to break out the parts of the statements in smaller portions for the kids separately so that we can check out time needed for each one accordingly. Then we will add the starting timing that is $ 12.00p.m $ , the thirty minutes break and the time they needed overall.

Complete step by step solution:
Breaking out the portions of the statements according to the work done by individuals.
It’s given that Rahul can finish his one-fifth work in $ 1 $ hour. So, the time Rahul need to complete his full homework is $ \dfrac{1}{{one - fifth}} = \dfrac{1}{{\dfrac{1}{5}}} = 5 $ hours.
Similarly, Neha can finish her three-seventh work in $ 1 $ hour $ 30 $ minutes that can be written as $ 1.5 $ hour. So, the time Neha need to complete his full homework is $ \dfrac{{1.5}}{{three - seventh}} = \dfrac{{1.5}}{{\dfrac{3}{7}}} = \dfrac{{1.5 \times 7}}{3} = 3.5 $ hours that is equal to $ 3 $ hour $ 30 $ minutes.
For Riya, she can finish her three-fourth of her homework in $ 3 $ hour $ 30 $ minutes that can be written as $ 3.5 $ hour. So, the time Riya need to complete his full homework is $ \dfrac{{3.5}}{{three - fourth}} = \dfrac{{3.5}}{{\dfrac{3}{4}}} = \dfrac{{3.5 \times 4}}{3} = \dfrac{{14}}{3} = 4\dfrac{2}{3} $ hours that is equal to $ 4 $ hour $ 40 $ minutes.
Since, they began at $ 12.00p.m $ and also attended a break at $ 3.30p.m $ for $ 30 $ minutes.
So, Rahul started the work at $ 12.00p.m $ and also attended a break at $ 3.30p.m $ for $ 30 $ minutes and took $ 5 $ hours to complete it all.
Then accordingly,
Rahul can play at:
 $ 12.00p.m + 30\min + 5hrs = 12.00 + 00.30 + 5.00 = 5.30p.m $
Similarly, Neha can start playing at: $ 12.00p.m + 30\min + 3hr30\min = 12.00 + 00.30 + 3.30 = 4.00p.m $
And, Riya can start playing at:
 $ 12.00p.m + 30\min + 4hr40\min = 12.00 + 00.30 + 4.40 = 5.10p.m $ .
So, the correct answer is “Option B”.

Note: When minutes exceeds by sixty then one hour is added to the hour hand and sixty is subtracted from the minutes hand, similarly when seconds exceeds sixty then one minute is added to minutes place and sixty subtracted from seconds place.
 $ \dfrac{2}{3} $ hour is written as $ 40\min $ because, one hour is equal to sixty minutes so, $ \dfrac{2}{3} $ hour is written as:
  $
  1hr = 60\min \\
  \dfrac{2}{3}hr = \dfrac{2}{3} \times 60 = \dfrac{{2 \times 60}}{3} = \dfrac{{120}}{3} = 40\min \;
  $