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: 6,500 was divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs.30 less. Find the original number of persons.

Answer:

Let the number of person

Therefore

Hence the number of people is 50.

Question 6: A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hr from its usual speed find its usual speed.

Answer:

Let the speed of the plane

Therefore

Hence the original speed of the plan is 750 km/hr.

Question 7: Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.

Answer:

Let the speed of the second train

Speed of the first train

Given

Speed of the first train is 20 km/hr. Speed of the second train is 15 km/hr.

Question 8: The sum S of first n even natural numbers is given by the relation S=n(n+1). Find n, if the sum is 420.

Answer:

Hence n = 20

Question 9: The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.

Answer:

Let the age of father

Therefore Age of son

Age of father 5 years ago

Age of son 5 years ago

Given

Hence father’s age is 36 years and son’s age is 9 years.

Question 10: 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 11: Mohan takes 16 days less than Manoj to do a piece of work. If both working together can do it in 15 days, in how many days will Mohan alone complete the work?

Answer:

No of days that Manoj takes to complete the work

Therefore the number of days Mohan takes to complete work

Given

Therefore Mohan will take 24 days to complete the work.

Question 12: Two years ago, a man’s age was three times the square of his son’s age. In three years of time, his age will be four times his son’s age. Find their present ages.

Answer:

Let man’s age now

Let son’s age now

Given

Solving

Hence the fathers age is 29 years.

Question 13: In certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by 1/14. Find the fraction.

Answer:

Let the fraction

Given

Therefore the fraction is

Question 14: In a two-digit number, the ten’s digit is bigger. The product of the digit is 27 and the difference between two digits is 6. Find the number.

Answer:

Let the number be

Therefore the number is 93

Question 15: Some school children went on an excursion by a bus to a picnic spot at a distance of 300 km. while returning, it was raining and the bus had to reduce its speed by 5 km/hr and it took two hours longer for returning. Find the time taken to return.

Answer:

Let the speed of the bus is

Given

Hence the speed of the bus was 30 km/hr $

Therefore the time taken to return

Question 16: 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