# Important Questions for Class 8 Chapter 13-Direct and Inverse Proportions

We have come up with sets of important CBSE questions across grades that are based on the latest syllabus and exam pattern. It will help you to prepare well for your final exams or any other competitive exams.

**Important questions based on NCERT syllabus for Class 8 Chapter 13-Direct and Inverse Proportions:**

*Question 1*: In a school, there are 8 periods per day each of 1 hour duration. How long would each period be, if 4 more periods are to be added, assuming the number of school hours to be same?

*Solution*:

If 4 more periods are added, the total no. of periods becomes 12.

As number of periods increase, period duration decreases. This is the case of inverse proportion.

We know that the number of periods x period duration = constant

8 × 60 = 12 × d

d = 40 minutes.

So the duration of each period = 40 minutes.

*Question 2*: If the weight of 12 sheets of paper is 40 grams, how many sheets of paper will be present in 5 kg of a paper bundle?

*Solution*:

If x and y are in direct proportion, x/y = Constant

As number of papers and weight are in direct proportion,

12/40 = n/5000

n = 1500

There will be 1500 papers in the bundle.

*Question 3*: A certain number of men can finish a piece of work in 100 days. If how ever, there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally ?

*Solution*:

Now number of men is inversely proportional to the no. of of days

∴ x × 110 = (x − 10)100

x × 110 = (x − 10)100

⇒ 110x = (x − 10)100 = 100x − 1000

⇒ 110x = 100x - 1000

⇒ 1000 = 110x − 100x

∴ 1000 = 10x

100 = x

*Question 4*: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds and crosses the man in 8 seconds. Find the length of the train.

*Solution*:

Let length of train = x m

∴ Distance covered to cross the bridge

= (180 + x)m

Distance covered to cross the man = x m

∵ speed is constant

∴ Distance covered is directly proportional to the time taken.

⇒ (180 + x)/20 = x/8

⇒ (180 + x)/20 = x/8

⇒ 8(180 + x) = 20x

⇒ 1440 + 8x = 20x

⇒ 1440 = 20x − 8x

⇒ 1440 = 12x

⇒ 1440/12 = x

⇒ 120 = x

Hence the length of the train

= 120 m