MATHEMATICS [3 marks sum]

The count of bacteria in a culture grows by 10% during first hour, decreases by 8% during second hour and again increases by 12% during third hour. If the count of bacteria in the sample is 13125000, what will be the count of bacteria after 3 hours?

A mango tree was planted 2 years ago. The rate of its growth is 20% per annum. If at present, the height of the tree is 162 cm, what it was when the tree was planted?

The population of a town is increasing at the rate of 10% per annum. If its present population is 36300, find:
(i) its population after 2 years,
(ii) its population 2 years ago.

The value of a machine depreciates 10% annually. Its present value is ₹64800. Find:
(i) its value after 2 years,
(ii) its value 2 years ago.

Amit started a shop by investing ₹500000. In the first year, he incurred a loss of 5%. However, during the second year, he earned a profit of 10% which in the third year rose to 12%. Calculate his net profit for the entire period of three years.

In a factory, the production of scooters was 40000 per year, which rose to 57600 in 2 years. Find the rate of growth per annum.

Calculate the amount and the compound interest on ₹ 16000 for 1 year at 15% per annum, compounded half-yearly.

If the simple interest on a sum of money for 3 years at 8% per annum is ₹ 7500, find the compound interest on the same sum, for the same period at the same rate.

How much will ₹ 12000 amount to in 2 years at compound interest, the rates of interest for the successive years being 10% and 11% respectively?

At what rate per cent per annum will ₹ 3000 amount to ₹ 3993 in 3 years, the interest being compounded annually?

The difference between the simple interest and the compound interest on a sum of money for 2 years at 12% per annum is ₹216. Find the sum.

What sum of money will amount to ₹ 93170 in 3 years at 10% per annum, compounded annually?

What sum of money will amount to ₹ 18150 in 2 years at 10% per annum, compounded annually?

Calculate the amount and the compound interest on ₹ 15000 for 2 years compounded annually, the rates of interest for the successive years being 8% and 9% per annum respectively.

Calculate the amount of ₹ 30000 at the end of 2 years 4 months, compounded annually at 10% per annum.

Mr. Ravi borrows ₹ 16,000 for 2 years. The rate of interest for the two successive years are 10% and 12% respectively. If he repays ₹ 5,600 at the end of first year, find the amount outstanding at the end of the second year.

A man borrows ₹ 15000 at 12% per annum, compounded annually. If he repays ₹ 4400 at the end of each year, find the amount outstanding against him at the beginning of the third year.

Sudhakar borrows ₹ 22500 at 10% per annum, compounded annually. If he repays ₹ 11250 at the end of first year and ₹ 12550 at the end of the second year, find the amount of loan outstanding against him at the end of the third year.

A man invests ₹ 10000 for 3 years at a certain rate of interest, compounded annually. At the end of one year, it amounts to 11200. Calculate:
(i) the rate of interest per annum;
(ii) the interest accrued in the second year;
(iii) the amount at the end of the third year

Rohit borrows ₹ 62500 from Arun for 2 years at 10% per annum, simple interest. He immediately lends out this sum to Kunal at 10% per annum for the same period, compounded annually. Calculate Rohit's profit in the transaction at the end of two years.

The simple interest on a sum of money for 2 years at 10% p.a. is ₹ 1700. Find:
(i) the sum of money,
(ii) the compound interest on this sum for 1 year, payable half-yearly at the same rate.

Find the amount and the compound interest on ₹ 10000 for 1 year at 12% per annum, compounded half-yearly.

Peter invested ₹ 240000 for 2 years at 10% per annum compounded annually. If 20% of the accrued interest at the end of each year is deducted as income tax, find the amount he received at the end of 2 years.

Calculate the amount and the compound interest on ₹ 25000 for 3 years, compounded annually, the rates of interest for the successive years being 8%, 9% and 10% respectively.

Calculate the amount and the compound interest on ₹ 25000 for 2 years at 8% per annum, compounded annually.

The simple interest on a sum of money at 12% per annum for 1 year is ₹ 900. Find
(i) the sum of money and
(ii) the compound interest on this sum for 1 year, payable half-yearly at the same rate.

The population of a town was decreasing every year due to migration. The present population of the town is ₹ 6,31,680. Last year the migration was 4% and the year before last, it was 6%, What was the population 2 years ago?

Mr Goyal bought a car for ₹ 6,25,000. Its value depreciates at 20% p.a. How many years it would take for the price of the car to go down by ₹3,69,000?

A mango tree was planted 2 years ago. The rate of its growth is 20% per annum. If at present, the height of the tree is 162 cm, what it was when the tree was planted?

The population of a town is 64000. If the annual birth rate is 11.7% and the annual death rate is 4.2%, calculate the population of the town after 3 years.
[Hint: Net growth rate = (11.7 - 4.2)% = 7.5%]

At what rate per cent per annum will ₹ 3000 amount to ₹ 3993 in 3 years, the interest being compounded annually?

What sum of money will amount to ₹ 93170 in 3 years at 10% per annum, compounded annually?

What sum of money will amount to ₹ 18150 in 2 years at 10% per annum, compounded annually?

If the simple interest on a sum of money for 3 years at 8% per annum is ₹ 7500, find the compound interest on the same sum, for the same period at the same rate.

Calculate the amount and the compound interest on ₹ 10000 for 2 years at 8% р.а., compounded annually.

Find the amount and the compound interest on ₹ 10000 for 1 year at 12% per annum, compounded half-yearly.

Peter invested ₹ 240000 for 2 years at 10% per annum compounded annually. If 20% of the accrued interest at the end of each year is deducted as income tax, find the amount he received at the end of 2 years.

Calculate the amount and the compound interest on ₹ 25000 for 3 years, compounded annually, the rates of interest for the successive years being 8%, 9% and 10% respectively.

Mr. Ravi borrows ₹ 16,000 for 2 years. The rate of interest for the two successive years are 10% and 12% respectively. If he repays ₹ 5,600 at the end of first year, find the amount outstanding at the end of the second year.

A man invests ₹ 10000 for 3 years at a certain rate of interest, compounded annually. At the end of one year, it amounts to ₹ 11200. Calculate:
(i) the rate of interest per annum;
(ii) the interest accrued in the second year;
(iii) the amount at the end of the third year.