Find the total number of prime factors in 16¹⁵ × 15²⁴ × 7¹⁵

In an examination, 65% of the total examinees passed. If the number of failures is 420, what is the total number of examinees?

 In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal? 

A constable is 114 meters behind a thief. The constable runs 21 meters and the thief runs 15 meters in a minute. In how much time will the constable catch the thief?

A man could buy a certain number of notebooks for Rs. 300. If the price of each notebook were Rs. 5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook.

Two pipes A and B can fill an empty tank in 30 minutes and 45 minutes respectively. If both the pipes are opened simultaneously, how long will it take to fill the empty tank?

 For a scholarship, at most n candidates out of 2n+12n+1 can be selected. If the number of different ways of selection at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is: 

A and B started a partnership business investing some amount in the ratio of 3: 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained.

A granary has rice, wheat, and maize that needs to be distributed in sacks. The quantity of rice is 18,000 kg, the quantity of wheat is 9,600 kg, and the quantity of maize is 3,600 kg. Find the minimum number of sacks required if each sack should have the same quantity of all the grains.