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Four paint brushes-A, B, C and D are used to paint or distort a sheet. A is twice as fast as B, C is twice as fast as D and B is 3/2 as fast as C. A distorts (1/8)th of the sheet, B distorts (1/4)th, C paints (3/8)th and D paints the rest. Only one paint brush can work at a time. It takes a total of 120 hours to paint the sheet. What is the time taken by C and D to paint the sheet?

Four paint brushes-A, B, C and D are used to paint or distort a sheet. A is twice as fast as B, C is twice as fast as D and B is 3/2 as fast as C. A distorts (1/8)th of the sheet, B distorts (1/4)th, C paints (3/8)th and D paints the rest. Only one paint brush can work at a time. It takes a total of 120 hours to paint the sheet. What is the time taken by C and D to paint the sheet? Correct Answer 540

Given:

A is twice as fast as B, C is twice as fast as D and B is 3/2 as fast as C.

Assumption:

Let the time taken by A, B, C and D to fill or distort the sheet be t, 2t, 3t and 6t respectively.

Calculation:

A distorts(1/8)th part of the sheet.

Time taken by A to paint= t × (1/8) = t/8

∴ Total time to paint the sheet = - (t/8) – (2t) (1/4) + (3t) (3/8) + (6t)(1/4)

⇒ 2t = 120 hours

⇒ t = 60 hours

Now,

Time taken by C and D to paint the sheet= 3t + 6t = 9t = 540

∴ The time taken by C and D to paint the sheet is 540 hours.

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