Paper 1 · Mathematical Reasoning and Aptitude
UGC NET June 2023 (17.06.2023) Shift-II
A and B can together complete a task in 20 hours. After 5 hours A leaves, and B takes 45 hours to finish the remaining task. How many hours would A have taken to complete the entire task if he worked alone from the beginning?
A30 hours ✓ Correct
B40 hours
C48 hours
D60 hours
Correct answer: (A) 30 hours — A alone would take 30 hours, so the answer is 30 hours.
Explanation
★A alone would take 30 hours, so the answer is 30 hours.
★Together A and B do one-twentieth of the task per hour.
★In 5 hours together they finish 5 by 20, which is one-fourth of the task.
★So three-fourths of the task remains for B, who takes 45 hours to do it.
★So B alone does three-fourths in 45 hours, meaning the whole task in 60 hours.
★So B does one-sixtieth per hour, and A does one-twentieth minus one-sixtieth, which is one-thirtieth.
★So A alone would take 30 hours.
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