In a culture , the bacteria count is 1,00,000. The number is increased by `10%` in 2 hours. In how many hours will the count reach 2,00,000. If the rate of growth of bacteria is proportional to the number present ?

The population of a country doubles in 50 years. How many years will it be five times as much? Assume that the rate of increase is proportional to the number inhabitants. (hint: log2=0.6931, log5=1.6094)

Given the numbers 1,2,3,4,5. How many 5 digit numbers greater than 24,000 can be formed if repetition is not allowed?

Suppose two Cars start together in the same direction from the same place. The first goes with uniform speed of 10km//hr. The second goes at a speed of 8km//hr in the first hour and increases the speed by 1//2km each succeeding hour.After how many hours will the second car overtake the first car if both cars go non-stop?

What is the interest for 16,000 rupees at 12 1/2 % for one year? What would be the interest if the rate of interest is only 6 1/4 % ?

Given the numbers 1,2,3,4,5. How many 5 digit numbers in between 23,000 and 30,000 can be formed if repetition is not allowed?

How many numbers can be formed from the digits 1,2,3 and 9 if repetition of digits is not allowed?

A student builds square pattern with square bricks using the following sequence of steps. The number of bricks used in the Ist stage is 1,the number of additional bricks used in the 2nd stage is 3, the number of additional bricks used in the 3rd stage is 5 and son on .How many additional bricks does the student use in the 5th stage ?

In factory there are two machines A and B producing toys.They respectively produce 60 and 80 units in one hour.A can run a maximum of 10 hours and B a maximum of 7 hours a day .The cost of their running per hour respectively amount to 2,000 and 2,500 rupee.The total duration of working these machines cannot exceed 12 hours a day.If the total cost cannot exceed Rs. 25,000 per day and the total daily production is atleast 800 units,then formulate the problem mathematically.