Direct And Inverse Proportions Test

Result

Direct And Inverse Proportions Test - 5

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Question 1
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Rajan has just enough money to buy 24 pairs of jeans worth Rs. 700 each. How many pairs of jeans can he buy with the same amount if he gets a discount of Rs. 100 on each pair?

A
28

B
30

C
31

D
32

Solution

Let the number of jeans he can buy at discounted price be x.

No. of jeans 24 x

Cost of each pair of jeans Rs. 700 Rs. 600

It is a case of inverse proportion.

We know that two quantities, x and y, are said to be in inverse proportion if an increase in x causes a proportional decrease in y and vice-versa, in such a manner that the product of their corresponding values remains constant.

24 × 700 = (x) × 600
x = 28
Question 2
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Directions For Questions

Determine whether the given statements are true (T) or false (F) and choose the correct option accordingly.

...view full instructions

1) If x and y are in direct proportion, then x/y = constant.
2) As the diameter of a circle increases, the circumference also increases. This is a case of direct proportion.
3) If distance is constant, then work is inversely proportional to force.
4) In an inverse proportion, if one number increases, then the other will decrease.

A
1 - T, 2 - T, 3 - F, 4 - T

B
1 - T, 2 - F, 3 - T, 4 - F

C
1 - T, 2 - F, 3 - F, 4 - F

D
1 - F, 2 - T, 3 - T, 4 - F

Solution

1) If x and y are in direct proportion, then x/y = constant.
This is true because two quantities, x and y, are said to be in direct proportion if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.

2) As the diameter of a circle increases, the circumference also increases. This is a case of direct proportion. (True)
Circumference ∝ Diameter

3) If distance is constant, then work is inversely proportional to force.
This is false because: Work = Force x Distance

If distance is constant, then W = kF.
So, in this case, work is directly proportional to force.

4) In an inverse proportion, if one number increases, then the other will decrease.
This is true because we know that two quantities, x and y, are said to be in inverse proportion if an increase in x causes a proportional decrease in y and vice-versa, in such a manner that the product of their corresponding values remains constant.
Question 3
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Fill in the blanks:

1) When two quantities are in direct proportion, as one increases, the other increases by the same _____.
2) For some constant k, if xy = k, then the values of x and y vary ____.
3) When two given quantities vary directly, an increase in one will reflect as ____ in the other quantity.

A
1- percentage, 2- directly, 3- a decrease

B
1- percentage, 2- inversely, 3- an increase

C
1- value, 2- inversely, 3- no change

D
1- value, 2- directly, 3- no change

Solution

1) When two quantities are in direct proportion, as one increases, the other increases by the same percentage/value.
2) For some constant k, if xy = k, then the values of x and y vary inversely.
3) When two given quantities vary directly, an increase in one will reflect as an increase in the other quantity.