Home › SSC CGL › Quantitative Aptitude › Time and Work › **Time and Work — formulas used here.** - Work d…
**Time and Work — formulas used here.** - Work done in unit time. If a worker finishes a job in $m$ days, the fraction of work done in one day is $\tfrac{1}{m}$. - Combined work (two workers). A finishes in $X$ days, B in $Y$ days; together they finish in $\tfrac{XY}{X+Y}$ days. - Combined work (three workers). A, B, C take $X$, $Y$, $Z$ days; together they take $\tfrac{XYZ}{XY+YZ+ZX}$ days. - Efficiency–time inverse. If A is $k$ times as efficient as B, A takes $\tfrac{1}{k}$ as long. - Workforce equivalence. $M_1 D_1 T_1 = M_2 D_2 T_2$ for the same work, where $M$ = workers, $D$ = days, $T$ = hours/day. **Question.** A and B together can finish a job in 6 days. B alone finishes the same job in 15 days. How long does A take alone?
A$8$ days
B$9$ days
C$10$ days
D$12$ days
Answer & Solution
Correct answer: C. $10$ days
A's one-day work = (combined) − (B's). $\tfrac{1}{A} = \tfrac{1}{6} - \tfrac{1}{15} = \tfrac{5 - 2}{30} = \tfrac{1}{10}$. So A alone takes $10$ days. Option B (9) and D (12) come from algebra slips; C is the consistent answer.
Related questions
A and B together complete a work in 12 days. A alone in 18 days. How long does B alone takRohan and Rohit together can finish a job in 10 days, while Rohan alone can do it in 15 daA and B together finish a task in 1.5 days, but A left early and the task took 2 days in aTrij can paint a wall alone in 7.2 days while Madhu takes 10.8 days for the same work. WorIf 200 men can construct a building in 1024 days, how many men are needed to construct theTwo persons Kuldeep and Agarkar can reap a field in 8 and 12 hours respectively. They workA pipe can fill a tank in 15 hours. Due to a leak at the bottom, it takes 20 hours to fill10 men can finish painting a wall in 8 days. How many more men are needed to finish the sa