Question : G1 can do a piece of work alone in 20 days, G2 can do the same piece of work alone in 40 days, and G3 can do it alone in 60 days. They worked together and completed the work. If the combined share received by G1 and G2 is INR 2,700, then what is the total amount received by all the 3 workers taken together?
Option 1: INR 3,300
Option 2: INR 3,000
Option 3: INR 3,900
Option 4: INR 3,600
Correct Answer: INR 3,300
Solution :
LCM of 20, 40 and 60 is 120.
Let the total work = 120 units
Efficiency of G
1
$=\frac{120}{20} = 6$
Efficiency of G
2
$=\frac{120}{40} = 3$
Efficiency of G
3
$=\frac{120}{60} = 2$
The share is distributed according to their efficiencies.
Let their share be $6x,3x$ and $2x$.
According to the question,
$6x+3x=2700$
$\therefore x=300$
Total amount received by all three workers $=6x+3x+2x = 11x=11\times300=3300$
Hence, the correct answer is INR 3,300.
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