Question

A and B can complete some work in 20 days, b and c in 15 days and C and A in 12 days. In how many days will they complete the work together?

Answer 1

Step-by-step explanation:

According to question,

A and B can do a work in 12 days

∴ (A + B)’s one day’s work = \frac{1}{12}

Similarly, (B + C)’s one day’s work = \frac{1}{15}

and (C + A)’s one day’s work = \frac{1}{20}

On adding all three,

∴ 2 (A + B + C)’s one day’s work = \frac{1}{12}+ \frac{1}{15}+ \frac{1}{20}

= \frac{10+8+6}{120} = \frac{1}{5}

and (A + B + C)’s one day’s work = \frac{1}{10}

∴ A, B and C together can complete the work in 10 days.

Answer 2

Answer:

According to question,

A and B can do a work in 12 days

∴ (A + B)’s one day’s work = 1/12

Similarly, (B + C)’s one day’s work = 1/15

and (C + A)’s one day’s work = 1/20

On adding all three,

∴ 2 (A + B + C)’s one day’s work = 1/12+1/15+1/20

= 10+8+6/120 = 1/15

and (A + B + C)’s one day’s work = 1/10

∴ A, B and C together can complete the work in 10 days