Question 1: A man saved Rs. in ten years. In each year after the first, he saved Rs. more than he did in the preceding year. How much did he save in the first year?

Answer:

Let the amount in Rs saved by the man in the first year

Rs. in the first year.

Question 2: A man saves Rs. during the first year, Rs. in the second year and in this way he increases his savings by Rs. every year. Find in what time his saving will be Rs. .

Answer:

Rs. in 5 year.

Question 3: A man arranges to pay off a debt of Rs. by annual instalments which form an arithmetic series. When of the installments are paid, he dies leaving one-third of the debt unpaid, find the value of, the first installment.

Answer:

Let the first instalment be and the common difference be . Therefore

… … … … … i)

In the first instalments, the man has paid Rs. Therefore

… … … … … ii)

Solving i) and ii) we get

Substituting in i) we get

Question 4: A manufacturer of radio sets produced units in the third year and units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in years and (iii) the product in the year.

Answer:

… … … … … i)

… … … … … ii)

Solving i) and ii) we get

i) Production in first year units

ii)

iii)

Question 5: There are trees at equal distances of meters in a line with a well, the distance of the well from the nearest tree being meters. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.

Answer:

The series will be

The total distance the gardener will cover in order to water all the trees m.

Question 6: A man is employed to count Rs. . He counts at the rate of Rs. per minute for half an hour. After this, he counts at the rate of Rs. less every minute than the preceding minute. Find the time taken by him to count the entire amount

Answer:

Amount of Rs. counted in first 30 minutes Rs.

Amount of money left for counting Rs.

Therefore the series would be or

Let the time taken to count the rest of the money be n minutes

Therefore the time taken to count is minutes.

Hence the total time taken to count the money minutes.

Question 7: A piece of equipment cost a certain factory Rs. . If it depreciates in value, the first, the next year, the third year, and so on. What will be its value at the end of years, all percentages applying to the original cost ?

Answer:

The percentage of depreciation of years is

Therefore total depreciation percentage is

Therefore the value at the end of year Rs.

Question 8: A farmer buys a used tractor for Rs. . He pays Rs. cash and agrees to pay the balance in annual instalments of Rs. plus interest on the unpaid amount. How much the tractor cost him?

Answer:

Cost of the tractor

Unpaid amount

The farmer pays Rs. per month. This means that the farmer will pay the remaining principal in instalments.

But he also has to pay the interest on the remaining principal at .

Therefore the interest paid would be represented by a series i.e.

Therefore the total cost of the tractor

Question 9: Shamshad Ati buys a scooter for Rs. . He pays Rs. cash and agrees to pay the balance in annual instalments of Rs. plus interest on the unpaid amount. How much the scooter will cost him.

Answer:

Cost of the scooter

Unpaid amount

The farmer pays Rs. per month. This means that the farmer will pay the remaining principal in instalments.

But he also has to pay the interest on the remaining principal at .

Therefore the interest paid would be represented by a series i.e.

Therefore the total cost of the scooter

Question 10: The income of a person is Rs. in the first year and he receives an increase of Rs. to his income per year for the next years. Find the total amount, he received in years.

Answer:

Therefore total amount received

Question 11: A man starts repaying a loan as the first installment of Rs. . If he increases the instalments by Rs. every month , what amount he will pay in the instalment?

Answer:

Therefore the instalment

Question 12: A carpenter was hired to build window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

Answer:

Therefore the carpenter will take days to complete the task.

Question 13: We know that the sum of the interior angles of a triangle is . Show that the sums of the interior angles of polygons with sides form an arithmetic progression. Find the sum of the interior angles for a sided polygon.

Answer:

We know that:

The sum of interior angles of a polygon with sides

The sum of interior angles of a polygon with sides

The sum of interior angles of a polygon with sides

Since the sum of the interior angles with sides , then the sum of sided polygon would be

The sum of the interior angles for a sided polygon

Question 14: In a potato race potatoes are placed in a line at intervals of meters with, the first potato meters from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?

Answer:

Therefore the contestant would run meters to bring back all the potatoes.

Question 15: A man accepts a position with an initial salary of Rs. per month. It is understood that he will receive an automatic increase of Rs. in the very next month and each month thereafter.

i) Find his salary for the tenth month

ii) What is his total earnings during the first year?

Answer:

i)

Therefore month salary

ii)

Therefore the total earnings in the first year

Question 16: A man saved Rs. in years. In each succeeding year after the first year, he saved Rs. more than what he saved in the previous year. How much did he save in the first year?

Answer:

Let the savings for the first year

in the first year.

Question 17: In a cricket team tournament teams participated. A sum of Rs. is to be awarded among themselves as prize money. If the last-placed team is awarded Rs. in prize money and the award increases by the same amount for successive winning places, how much amount would the first team receive?

Answer:

Given:

Therefore the winner will get