Two friends A and B take a job for Rs. 8000. Had they worked alone, A would have taken 15 days while B would have taken 40 days. They started working together but after 6 days, A left and B completed the remaining work alone. Find the difference between their share.
1). Rs. 3200
2). Rs. 4800
3). Rs. 1600
4). Can’t be determined
Let the total work be LCM of (15, 40) = 120 units
Efficiency of A = 120/15 = 8 units/days
Efficiency of B = 120/40 = 3 units/days
Now, since they work for different number of days, the amount of Rs. 8000 will be divided in the ratio of units of work done.
Work done by A in 6 days = 6 × 8 = 48 units
Work done by B in 6 days = 6 × 3 = 18 units
Remaining work = 120 – (48 + 18) = 120 – 66 = 54 units
? These 54 units of work will be done by B alone.
∴ Total work done by B = 18 + 54 = 72 units
Ratio of work done by A and B = 48 ? 72 = 2 ? 3
∴ Amount received by A = 8000 × 2/5 = Rs. 3200
And amount received by B = 8000 × 3/5 = Rs. 4800
Required difference = 4800 – 3200 = Rs. 1600