Page 151 - Maths Skills - 8

Direct and Inverse Proportions 149

(iii) More men working on a project, the shorter is Q.2. Assertion (A): If the number of workers
the time to complete it. increases, the time required to complete the
(iv) None of these. work will decrease.
Answer the following questions on the basis of Reason (R): The time required to complete a
the above data. piece of work is inversely proportional to the
1. Which of the above phrases are the examples number of workers.
of direct variation?
2. If P varies inversely as Q then complete the SUBJECTIVE TYPE QUESTIONS
table given below: F. Solve the following word problems

P – 6 1. Priyanka cycles to her school at an average speed
Q 2 3 of 14 km/h. It takes her 20 minutes to reach the
school. If she wants to reach her school in 10
E. Assertion-Reason Based Questions minutes, what should be her average speed?
Directions for Questions 1 to 2: In each of the 2. Reading 5 hours a day, Dinesh can finish a book
questions given below, there are two statements in 10 days. How many hours a day should he
marked as Assertion (A) and Reason (R). Mark your read to finish the book in 8 days?
answer as per the codes provided below:
(a) Both A and R are true and R is the correct 3. Three taps A, B and C can fill up an empty tank
in 6, 8 and 12 hours respectively. After 2 hours
explanation of A. taps B and C are closed. How much time will A
(b) Both A and R are true but R is not the correct take to fill the remaining part of a tank?
explanation of A.
(c) A is true but R is false. 4. A train having a length of 105 m crosses a
railway platform in 20 sec. If the length of the
(d) A is false but R is true. platform is 65 m, find the speed of the train.
Q.1. Assertion (A): The expense of buying fair tickets 5. Two trains 200 m and 400 m long are moving
is directly proportional to the number of people in opposite directions on parallel tracks. If their
watching the fair. speeds be 25 km/h and 29 km/h respectively,

Reason (R): This is an example of direct how long would it take the faster train to pass
variation, where an increase in one variable the slower train?
leads to an increase in the other variable.

HOTS

1. 600 soldiers in a fort had enough food for 30 days. After 6 days, some soldiers were sent to another fort and
thus the food lasted for 40 more days. How many soldiers left the fort?

2. If 8 persons can weave 160 shawls in 5 days, how many shawls will be woven by 3 persons in 14 days?
3. To do a certain work, B would take three times as long as A and C together and C twice as long as A and
B together. The three men together complete the work in 10 days. How long would each take separately to
complete the work?

4. Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened
simultaneously, after how much time should B be closed so that the tank is full in 18 minutes