Multiple choice

$A$ and $B$ can do a piece of work in $5$ days, $B$ and $C$ can do it in $7$ days. $A$ and $C$ can do it in $4$ days. Who among these will take the least time if put to do it alone ?

  1. $A$
  2. $B$
  3. $C$

  4. Data inadequate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given (A+B)=1/5, (B+C)=1/7, (A+C)=1/4. Adding these gives 2(A+B+C) = 1/5+1/7+1/4 = 83/140, so (A+B+C) = 83/280. Subtracting (B+C) gives A = 83/280 - 40/280 = 43/280. Subtracting (A+C) gives B = 83/280 - 70/280 = 13/280. Subtracting (A+B) gives C = 83/280 - 56/280 = 27/280. Since A has the largest work rate (43/280), A takes the least time.

AI explanation

Let the total work be the LCM of 5, 7 and 4, which is 140 units. The daily work units are 28 for A and B combined, 20 for B and C combined, and 35 for A and C combined. Adding these three equations gives twice the combined daily work of A, B and C as 83 units, so their individual combined daily work is 41.5 units. Subtracting the pairs gives daily rates of 21.5 for A, 6.5 for B and 13.5 for C. A completes the 140 units in 140 divided by 21.5, which is about 6.51 days, the shortest time among the three.

Keep practicing — related questions