JIPMAT 2024 (QA) - A is 40 \% less efficient than B who can do the same work in 20 \% less time than C. If A and B together can complete 80 \% work in 12 days, then in how many days 60 \% work can be completed by B and C together ? | PYQs + Solutions

JIPMAT 2024

Arithmetic

Time & Work

Medium

A is $40 \%$ less efficient than $B$ who can do the same work in $20 \%$ less time than $C$ . If $A$ and B together can complete $80 \%$ work in 12 days, then in how many days $60 \%$ work can be completed by $\mathrm{B}$ and $\mathrm{C}$ together ?

2 days

4 days

8 days

16 days

Correct Option: 3

1) Given:

\newline

A is

40\%

less efficient than B:

A = 0.6B

\newline

B does work in

20\%

less time than C:

B = 1.25C

C = 0.8B

\newline

A and B complete

80\%

work in

12

days

2) Step 1: Calculate A and B's combined efficiency

\newline

Let total work be

100

units

\newline

Work done by A and B in 12 days =

80

units

\newline

Efficiency of

(A + B) = \frac{80}{12} = \frac{20}{3}

units/day

Combined efficiency:

A + B = 0.6B + B = 1.6B

Therefore:

1.6B = \frac{20}{3}

B = \frac{20}{3 × 1.6} = \frac{25}{6}

units/day

A = 0.6B = 0.6 × \frac{25}{6} = \frac{5}{2}

units/day

3) Step 2: Calculate B and C's combined efficiency

\newline

B + C = B + 0.8B = 1.8B

B + C = 1.8 × \frac{25}{6} = \frac{45}{6} = \frac{15}{2}

units/day

4) Step 3: Time for

60\%

work by B and C

Time =

\frac{\text{Work}}{\text{Efficiency}} = \frac{60}{\frac{15}{2}} = 60 × \frac{2}{15} = 8

days