SSC & BANK EXAMS: QUANTITATIVE APTITUDE · TIME & WORK

Time and work: two people together

Together time = ab/(a + b). Or use the LCM method: total work = LCM of days, add the daily units.

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Worked examples

Example 1 · level 1

Harpreet can paint a house in 24 days and Vihaan can paint it in 12 days. Working together, in how many days will they finish it?

Show solution

Total work = 24 units.
Together per day = 1 + 2 = 3 units.
Days = 24 ÷ 3 = 8.

Answer: 8 days

Example 2 · level 2

Tenzin and Diya together can complete a project in 11 days. Tenzin alone can complete it in 22 days. In how many days can Diya alone complete it?

Show solution

Work = 22 units. Together = 2/day, Tenzin = 1/day.
Diya = 1 units/day.
Diya alone = 22 ÷ 1 = 22 days.

Answer: 22 days

Example 3 · level 3

Aditya can complete a piece of work in 15 days and Joseph in 30 days. They work together for 9 days, then Aditya leaves. In how many more days will Joseph finish the remaining work?

Show solution

Work = 30 units; Aditya = 2/day, Joseph = 1/day.
Together for 9 day(s): 27 units. Left: 3 units.
Joseph needs 3 ÷ 1 = 3 days.

Answer: 3 days