Dear Reader, Below are three problems involving work,time and ratios.

Question 1

Mayur Sait can complete making of a sofa set consisting of three pieces in 60 hours. He was able to complete this job in 40 hours with the assistance of Ganguly. If Mayur Sait received Rs.12600 as his share for the work done, how much would both Mayur and Ganguly would have charged for this work?

a) Rs.18900 b) Rs.25200 c) Rs16000 d) none of these.

Answer : Rs. 18900

Solution :

Mayur Sait can complete the work in 60 hours. But he had completed the work in 40 hours working along with Ganguly.
So Mayur Sait has done 40/60 of the work. i.e. 2/3 of the work He received Rs.12600.
1/3 of the work was done by Ganguly . For 2/3rd of the work, payment was Rs.12600. Therefore the payment for completing the work can be calculated as follows

Amount of Work            Payment
2/3                        12600
1                           ?

Payment received by both for completing the work = 12600 x 3/2 = Rs.18900

Question 2

Gopalakrishna Gandhi can complete work of painting a house in 36 hours.Ramakrishna Mukhopadhyay can complete the same work of painting a house in 24 hours. Both of them work together and complete the painting work and receive Rs. 90000 as total contract amount, how much will Gopalakrishna Gandhi get out of this?

a) Rs. 54000 b) Rs.36000 c)Rs. 48000 d) none of these.

Answer : b) Rs. 36000

Solution :

Total contract amount = Rs.90000
Gopalakrishna Gandhi does in one day 1/36 of the work
Ramakrishna Mukhopadhyay does in one day 1/24 of the work.
Payment to be received and time taken are inversely proportional to each other.
i.e Payment of Gopalakrishna Gandhi / Payment of Ramakrishna Mukhopadhyay = Time taken by Ramakrishna Mukhopadhyay / Time taken by Gopalakrishna Gandhi
= 24/36 = 2/3

Therefore Payment of Gopalakrishna Gandhi : Payment of Ramakrishna Mukhopadhyay = 2 : 3
Payment of Gopalakrishna Gandhi = 2 / (2 + 3) x Full Payment = 90000 x 2/5 = Rs.36000 (This is our answer)
Payment of Ramakrishna Mukhopadhyay = 3 / (2 + 3) x Full Payment = 90000 x 3/5 = Rs.54000

Question 3

Venkatesan can complete a job in 48 hours. Balajee can complete the same job in 72 hours. Both of them worked together for twelve hours. A dispute arose between the two and Balajee left the work incomplete. Thereafter Venkatesan took the help of Adhvaith and completed the job in another 24 hours. The total compensation for the work done was Rs. 49200. How much Adhvaith has to be paid for the work done by him?

a) Rs.3600 b)Rs.2400 c)Rs.6400 d)Rs.4100

Answer : d) Rs. 4100

Solution :

Venkatesan can complete the job in 48 hours.
Work done by Venkatesan in 1 hour = 1/48
Balajee can complete the job in 72 hours.
Work done by Balajee in 1 hour = 1/72
Work done by Balajee and Venkatesan jointly in 1 hour = 1/48 + 1/72
Work done by both Balajee and Venkatesan in 12 hours = (1/48 + 1/72) x 12 = 5/12 of the work
Remaining work = 1 - 5/12 = 7/12

Thereafter Venkatesan completed the work in 24 hours with the help of Adhvaith.
In 24 hours Venkatesan would have done (1/48 x 24) of the work = 1/2
Originally balance work to be done = 7/12
Work completed by Venkatesan = 1/2
So Adhvaith should have done, 7/12 - 1/2 = 1/12th of the work
Total compensation = Rs. 49200
So Adhvaith’s share = 49200 x 1/12 = Rs.4100