Question 1: The distance by road between two towns A and B is 216 km, and by rail it is 208 km. A care 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 train. [1998]

Answer:

Time taken by the car to reach town B from A

The time taken by the train, to reach town B from A

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 x for the above situation and solve it for . [1999]

Answer:

Cost of one article

New Cost

Therefore

Therefore the number of articles bought is 24.

Question 3: A hotel bill for a number of people for 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 8.

Question 4: An Airplane traveled a distance of 400 km at an average speed of x 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:

The time taken for onward journey

The time taken for return journeys

Hence the speed of the airplane is 71.65 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 30 and each row has 30 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 20

Question 7: A car covers a distance of 400 km at 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

Therefore speed of the car is 60 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 x 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

Then the time taken to cover the distance hrs

The new speed of the car km/hr

Therefore the time taken to cover the distance hrs

Hence given

km/hr

Question 10: A two digit number is such that the products 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 year hence her age will be twice that of her son. Find i) the age of her son five year 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 shop keeper 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.

No of books bought

If the cost of the book was Rs.

The the number of books bought

Given

simplifying

.

Hence the cost of the book is 48 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.

Planned Budget per student

Number of student who actually went for the party

Actual food budget per student

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

Since

Therefore

Solving we get

Question 15: [2013]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 16: [2006]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 17: [2012]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

If we want only three significant figures than

Question 18: [2014]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

If we want only two significant figures than

Question 19: [2005]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 20: [2004]

Answer:

Comparing with , we get

Since

Therefore

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:

Given

Simplifying:

Compare with equation , we get and

We know,

Therefore

Answer correct to two significant figures: