Answer: Option B
Let us assume that the total work to be done is 1 unit.
We are given that X can do the work alone in 5 days, which means that X can do 1/5th of the work in a day.
Similarly, Y can do 1/6th of the work in a day, and Z can do 1/7th of the work in a day.
When X, Y, and Z work together, their combined work in a day is the sum of their individual work in a day:
1/5 + 1/6 + 1/7 = (42 + 35 + 30) / 105 = 107/105
This means that X, Y, and Z together can complete the work in 105/107 days.
We are also given that they are paid Rs 53.50 for the work they did.
Now, we can use the formula:
Payment = (Work done by a person / Total work) * Total Payment
Let us calculate how much each person should be paid.
X's work in 1 day = 1/5So, his work in 105/107 days = (105/107) * (1/5) = 21/107
Y's work in 1 day = 1/6So, his work in 105/107 days = (105/107) * (1/6) = 17.5/107
Z's work in 1 day = 1/7So, his work in 105/107 days = (105/107) * (1/7) = 15/107
Now, we can use the above formula to calculate their payments:
X's payment = (21/107) / 1 * 53.50 = Rs 10.50 + Rs 10.50 = Rs 21Y's payment = (17.5/107) / 1 * 53.50 = Rs 8.75 + Rs 8.75 = Rs 17.50Z's payment = (15/107) / 1 * 53.50 = Rs 7.50 + Rs 7.50 = Rs 15
Therefore, the correct answer is Option B - Rs 21, Rs 17.50, Rs 15, and each person should be paid as calculated above.If you think the solution is wrong then please provide your own solution below in the comments section .