Anuj and Bishnu can complete a

Solution

ATQ,

Let the total work be = 144 units {LCM (24, 36 and 48) } Let the efficiency of 'Anuj', 'Bishnu' and 'Raj' be 'x' units/day, 'y' units/day and 'z' units/day, respectively. ATQ; (x + y) = 144 ÷ 24 Or, x + y = 6 ........ (I) (y + z) = 144 ÷ 48 Or, y + z = 3 ......... (II) And (z + x) = 144 ÷ 36 Or, x + z = 4 ............ (III) On adding equation (I) , (II) and (III) , we have; (x + y + y + z + x + z) = 6 + 3 + 4 Or, 2 × (x + y + z) = 13 So, x + y + z = 6.5 .......... (IV) On subtracting equation (I) from equation (IV) , we have; (x + y + z) - (x + y) = 6.5 - 6 Or, z = 0.5 Similarly, x = 3.5 and y = 2.5 So, work done by 'Anuj' in 8 days = (3.5 X 16) = 56 units And work done by 'Bishnu' in 12 days = (2.5 × 12) = 30 units So, work remaining = 144 - (56 + 30) = 58 units So, time taken by 'Raj' to finish the remaining work alone = 58 ÷ 0.5 = 116 days