Question 1: The distance by road between two towns A and B is 216 km, and by rail, it is 208 km. A car travels at a speed of and the train travels at a speed which is 16 km/hr faster than the car. Calculate;
The time taken by the car to reach town B from A, in terms of ;
The time taken by the train, to reach town B from A, in terms of .
If the train takes 2 hours less than the car to reach town B, obtain an equation in , and solve it.
Hence, find the speed of the train. [1998]
Answer:
Given that the train takes 2 hours less than the car to reach town B
Therefore speed of train
Question 2: A trader buys articles for a total cost of Rs.600. Write down the cost of one article in terms of
. If the cost per article were Rs.5 more, the number of articles that can be bought for Rs.600 would be four less. Write down the equation in terms of
for the above situation and solve it for
. [1999]
Answer:
Therefore
Therefore the number of articles bought is .
Question 3: A hotel bill for the number of people for an overnight stay is Rs.4,800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs.200. find the number of people staying overnight. [2000]
Answer:
Let the number of people
Therefore
Hence the number of people staying is .
Question 4: An Airplane traveled a distance of 400 km at an average speed of km/hr. on the return journey, the speed was increased by 40 km/hr. write down an expression for the time taken for The onward journey, The return journey. If the airplane takes 2 hours less in returning, calculate the speed of the airplane. [2002]
Answer:
Hence the speed of the airplane is km/hr
Question 5: In an auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. Find The number of rows in the original arrangement. The number of seats in the auditorium after re-arrangement. [2003]
Answer:
Let the number of rows
Therefore the number of seats in a row
Given
Therefore the number of rows are and each row has
seats.
Question 6: 480 is divided equally among children. If the number of children were 20 more then each would have got Rs.12 less. Find
[2011]
Answer:
Let the number of children
Therefore
Hence the number of children is
Question 7: A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car. [2012]
Answer:
Let the speed of the car be
Therefore speed of the car is km/hr.
Question 8: A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking as the smaller part of the two parts, find the number. [2010]
Answer:
Let the two parts be
Given
Also
Substituting it back
(ignore this as the number is positive)
Therefore the larger part is
Hence the number is
Question 9: By increasing the speed of the car by 10 km/hr, the time of the journey for a distance of 72 km is reduced by 36 minutes. Find the original speed of the car. [2005]
Answer:
Let the original speed of the car km/hr
hrs
The new speed of the car km/hr
hrs
Hence given
km/hr
Question 10: A two-digit number is such that the product of the digits is 6. When 9 is added to the number, the digits interchange their places. Find the number. [2014]
Answer:
Let the number by
Given … … … … … … i)
Also
… … … … … … ii)
Solving i) and ii)
Hence
Hence the number is
Question 11: Five years ago, a woman’s age was square of her son’s age. 10 years hence her age will be twice that of her son. Find i) the age of her son five years ago ii) the present age of the woman. [2007]
Answer:
Let the age of the son 5 years ago years
Therefore the woman’s age 5 years ago years
The present age of the son years
The present age of woman years
10 years hence the son’s age years
10 year hence the woman’s age year
Given that
solving
Hence
Therefore
The age of son 5 years ago years
The present age of the woman years.
Question 12: A shopkeeper buys a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that he could have bought for Rs. 960 would be 4 more. Taking the original cost of each book to be x Rs. write an equation in x and solve for it. [2013]
Answer:
Let the original cost of the book Rs.
If the cost of the book was Rs.
Given
simplifying
.
Hence the cost of the book is Rs.
Question 13: Some students planned a picnic. The budget for the food was Rs. 480. As eight of the students failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic. [2008]
Answer:
Let the number of students going to the picnic
Planned Food budget Rs.
Number of student who actually went for the party
Given
Simplifying
Hence the number of students who actually went for the picnic
Solve each of the following equations for
Question 14: [2007]
Answer:
Comparing with
, we get
Solving we get
Question 15: [2013]
Answer:
Comparing with
, we get
Solving we get
Question 16: [2006]
Answer:
Comparing with
, we get
Solving we get
Question 17: [2012]
Answer:
Comparing with
, we get
Solving we get
If we want only three significant figures than
Question 18: [2014]
Answer:
Comparing with
, we get
Solving we get
If we want only two significant figures than
Question 19: [2005]
Answer:
Comparing with
, we get
Solving we get
Question 20: [2004]
Answer:
Comparing with
, we get
Solving we get
Question 21: Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal. [2010]
Answer:
Comparing with
, we get
For roots to be equal, we should have
Question 22: [2012]
Answer:
Comparing with
, we get
For roots to be equal, we should have
Question 22: Solve the following equation: Give your answer correct to two significant figures. [2011]
Answer:
Simplifying:
Compare with equation , we get
and
Therefore
Answer correct to two significant figures:
i would like to correct you that in the question no. 11 the equation will be 2(x+15)
I fixed it. Thank you for your contribution.
where are the questions from 2012 to 2020
I think you will find some of them them in the solved board question papers.