Solve the following mathematical problems:

What should be the values of a and b for which $64x^2-9a{x}^2+108x-b$ will be a perfect cube?

Solve the following mathematical problems.

A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2 respectively by weight, If 39 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes?

Solve the following mathematical problems.

Mr, Sakil leaves his office at a certain fixed time. If he walks at the rate 5 km per hour ( kmh) he is late by 7 minutes . If he walks at the rate 6 kmh, he reached office 5 minutes earlier.

Solve the following mathematical problems.

A man deposited Tk, 5000 with a bank that pays interest at the rate of 5% per annul even –six month. The man will withdraw Tk 500 from his principal plus any interest accrued at each six – month period. How much total interest can expect to receive?

Solve the following mathematical problems.

A man earned Tk. 5000 from interest and wages . If he doubles his investment and also gets 50% increased wages before, his earning will stand to Tk. 8,000 Determine the original income of the man both in terms of interest ans wages. 

Solve the following mathematical problems.

Twenty men can finish a piece of work in 30 days. After how many days should 5 men leave the work so that it may be finished in 35 days?