Question 1: The sum successive odd numbers starting from 3 is given by the relation: . Determine , if the sum is 168.

Answer:

Given

Question 2: A stone is thrown vertically downwards and the formula gives the distance, d meters, that is falls in t seconds. How long does it take to fall 420 meters?

Answer:

Given

Hence

Question 3: The product of the digits of a two-digit number is 24. If its unit’s digit exceeds twice its ten’s digit by 2; find the number.

Answer:

Let the number be

Given

Therefore

Hence

Therefore the number is

Question 4: The age of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?

Answer:

Let the number of years

Therefore

Hence the product of their ages be 304 in 5 years.

Question 5: One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Find their present ages.

Answer:

Let the age of father

Let the age of son

Given

Therefore

Therefore son’s age is 7 years and father’s age is 49 years

Question 6: The age of a father is twice the square of the age of his son. Eight years hence, the age of the father will be 4 years more than three times the age of the son. Find their present ages.

Answer:

Let the age of father

Let the age of son

Given

Therefore Son’s age is 4 years and Father’s ages is 32 years.

Question 7: The speed of a boat in still water is 15 km/hr. it can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.

Answer:

Speed of the boat

Let the speed of the stream

Therefore,

Hence the speed of the steam is 5 \ km/hr $

Question 8: A person sends his servant to the market to buy oranges worth Rs.15. The servant having eaten three oranges on the way, the person pays 25 paisa per orange more than a market price. Find the number of oranges received back by the person.

Answer:

Let the market price of the orange

Number of oranges bought by the servant

But the servant eats 3 oranges

Therefore the real cost of each orange for this person

Therefore

Hence the person receives 12 oranges

Question 9: 250 is divided equally among a certain number of children. If there were 25 children more, each would have received 50 paisa less. Find the number of children.

Answer:

Let the number of children

Therefore

Hence the number of children is 100

Question 10: An employer finds that if he increases the weekly wages of each worker more by Rs. 5 and employs five workers less, he increases his weekly wage bill from Rs. 3,150 to Rs. 3,250. Find the weekly wages of the workers.

Answer:

Let the number of workers

Let the weekly wage of the worker

Given

or

Solving i) and ii)

Hence the weekly wage of the workers is 45 Rs.

Question 11: A trader bought a number of articles for Rs.1,200. Ten were damaged and he sold each of the remaining articles at Rs.2 more than what he paid for it, thus getting a profit of Rs. 60 on the whole transaction.

Answer:

Let the number of articles bought

Total cost price

Cost of one article

Number of articles sold

Selling price of one article

Total Selling Price

Therefore

Question 12: The total cost price of a certain number of identical article is Rs.4800. by selling the article Rs.100 each, a profit equal to the cost price of 15 article is made. Find the number of articles bought.

Answer:

Let the number of articles

Therefore

Therefore the number of articles bought is 60