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 the 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
(not possible)
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
(not possible)
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,
(not possible)
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
But the servant eats 3 oranges
Therefore
(not possible)
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
Question 12: The total cost price of a certain number of identical articles is Rs.4800. by selling the article Rs.100 each, a profit equal to the cost price of 15 articles is made. Find the number of articles bought.
Answer:
Let the number of articles
Therefore
Therefore the number of articles bought is 60