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In a factory there are 4 workers. Divyanshu can do the assigned task in 25 days when working alone while Gurpreet takes twice the time taken by Shubhanshu. Shubhanshu is 50% more efficient than Manish. If the daily wage that is distributed among them is Rs.1540. What is the wage received by Gurpreet and Shubhanshu together, if Divyanshu and Manish can do the work in 75/8 days? 

In a factory there are 4 workers. Divyanshu can do the assigned task in 25 days when working alone while Gurpreet takes twice the time taken by Shubhanshu. Shubhanshu is 50% more efficient than Manish. If the daily wage that is distributed among them is Rs.1540. What is the wage received by Gurpreet and Shubhanshu together, if Divyanshu and Manish can do the work in 75/8 days?  Correct Answer Rs.900

Given:

Divyanshu and Manish can do the work in 75/8 days

Calculation:

Let the time taken by Manish to do the work be x days

∴ (1/25) + (1/x) = 8/75

⇒ 1/x = (8/75) – (1/25)

⇒ 1/x = (8 – 3)/75 = 5/75 or 1/15

⇒ x = 15

∴ Manish can do the work in 15 days

Shubhanshu is 50% more efficient than Manish

⇒ Time taken by Shubhanshu = 15 × (100/150) = 10 days

Gurpreet takes twice the time that of Shubhanshu

⇒ Time taken by Gurpreet = 10 × 2 = 20 days

∴ Ratio of time taken by Divyanshu, Manish, Shubhanshu and Gurpreet = 25 ∶ 15 ∶ 10 ∶ 20 = 5 ∶ 3 ∶ 2 ∶ 4      ----(LCM = 60)

⇒  Ratio of there efficiencies = 12 ∶ 20 ∶ 30 ∶ 15      

∴ Wage received by Gurpreet and Shubhanshu together 

⇒ {(30 + 15)/77} × 1540 = Rs.900

∴ The wage received by Gurpreet and Shubhanshu together is Rs. 900

 

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