Students can quickly understand the concept of “Direct Proportion” by using the direct proportion questions and answers. The questions provided here can help students grasp the concept more quickly. To help them comprehend more clearly, we have also included some practice questions. Additionally, you may double-check your answers with comprehensive explanations provided on our page for each question. To learn more about direct proportion, click here.

Direct Proportion Questions with Solutions

What is Direct Proportion?

According to the definition of direct proportion, “Two quantities are said to be in direct proportion if you increase one quantity, the other will also rise, and if you decrease one quantity, the other quantity will also decrease”. For instance, suppose there are two numbers, a and b, where “a” is the number of candies and “b” is the total amount of money spent. You will pay more money if you purchase more candy, and less money would be spent if you purchase fewer candies. This means that “a” and “b” are directly proportional to one another in this situation. The symbol for it is a ∝ b. Direct variation is another name for direct proportion.

1. Determine whether the following quantities vary directly or inversely with each other?

(i) Number of books purchased (a) and their price (b).

(ii) Area of land (x) and the cost of the land (y).

Solution:

(i) The number of books purchased (a) and their price (b)

As we know, if the number of books purchased increases, their price will also increase. Similarly, if we purchase fewer books, their price will decrease. Hence, the number of books purchased and their price are directly proportional.

Thus, a ∝ b.

(ii) Area of land (x) and the cost of the land (y).

The cost of the land will be more if its area increases. Similarly, the cost of land will be lesser if its area decreases. Hence, the area of land and the cost of the land is directly proportional.

Therefore, x ∝ y.

2. Given that both x and y vary directly from each other. If x = 10 and y = 15, which of the following pairs is not possible with respect to the value of x and y?

x = 2 and y = 3
x = 8 and y = 12
x = 15 and y = 20
x = 25 and y = 37.5

Solution:

Given that x and y are directly proportional.

Hence, x/y = k(constant)

So, x/y = 10/15 = 2/3 …(1)

Now, check with the options provided here.

(a) x = 2 and y = 3

x/y = 2/3 …(2)

Hence, (1) = (2)

(b) x = 8 and y = 12

x/y = 8/12 = 2/3 …(3)

Hence, (1) = (3)

(c) x = 15 and y = 20

x/y = 15/20 = 3/4 …(4)

Hence, (1) ≠ (4)

(d) x = 25 and y = 37.5

x/y = 25/37.5 = 2/3 …(5)

Hence, (1) = (5)

Therefore, option (c) x = 15 and y = 20 should not be a possible pair with respect to the values x and y.

3. Check whether the values “x” and “y” given the table are directly proportional.

x	7	9	13	21	25
y	21	27	39	63	75

Solution:

In the given table, the value of y is three times the value of x.

Hence, in all columns, we can observe that y = 3x, which is equal to y/x = 3

I.e.,

y/x = 21/7 = 3

y/x = 27/9 = 3

x/y = 39/13 = 3

x/y = 63/21 = 3

x/y = 75/25 = 3

Hence, the values “x” and “y” presented in the table are directly proportional.

4. If “a” varies directly as “b”, then find the value of “k” in the following table.

a	12	6
b	48	k

Solution:

Given that “a” and “b” are directly proportional.

Hence, a/b = k (constant)

From the given table,

a/b = 12/48 = 1/4.

Similarly in second column,

a/b = 6/k = 1/4.

Therefore,

k = 6 × 4

k = 24.

Hence, the value of k is 24.

I.e.,

a	12	6
b	48	24

5. Fill in the missing values in the table, such that “a” is directly proportional to “b”.

a	3	5	7	9
b	___	20	28	___

Solution:

Given that, “a” and “b” are directly proportional.

Let the unknown values be “x” and “y”

Hence,

a	3	5	7	9
b	x	20	28	y

From the given table, we can write

a/b = 3/x = 5/20 = 7/28 = 9/y

Now, compare 3/x = 5/20

Cross multiplying the above equation, we get

3(20) = 5(x)

5x = 60

x = 60/5 = 12.

Similarly, compare 7/28 = 9/y.

So, we get 7y = 28(9)

7y = 252

Hence, y = 252/7

y = 36

Hence, the unknown values are x = 12 and y = 36.

Therefore,

a	3	5	7	9
b	12	20	28	36

Also, read: Direct and Inverse Proportion.

6. Ramya purchased 97 meters of cloth that cost Rs. 242.50. What will the length of the cloth be if she purchased it for Rs. 302.50.

Solution:

As we know, the length of the cloth and its costs are directly proportional. Because if we purchase more, the cost will be higher. Similarly, if we purchase less, the cost will decrease.

Hence, we get

Length (in Meters)	97	x
Cost (in Rs)	242.50	302.50

Now, we have to find the value of “x”.

Since the length and cost of cloth are directly proportional, we can write

97/242.50 = x/302.50

Now, cross multiply the above equation, we get

242.50x = 97(302.50)

242.50x = 29342.5

Hence, x = 29342.5 / 242.50 = 121.

Hence, the length of the cloth is 121 meters, if she purchased it for Rs. 302.50.

Therefore,

Length (in Meters)	97	121
Cost (in Rs)	242.50	302.50

7. The area occupied by 10 postal stamps is 50 square centimeters. Hence, find the total area occupied by 100 such postal stamps.

Solution:

Given that,

The area occupied by 10 postal stamps = 50 cm²

Hence, the area occupied by 1 postal stamp = 50/10 = 5 cm².

Therefore, the area occupied by 100 postal stamps = 100 × 5 = 500 cm².

8. State whether the given statement is true or false:

‘If “a” and “b” are in direct proportion, then (a – 1) and (b – 1) are also in direct proportion”.

Solution:

The given statement is “False”

Justification:

We know that, if “a” and “b” are in direct proportion, we can write

a/b = k

Let us assume that a = 2 and b = 4

Hence, a/b = 2/4 = 1/2 …(1)

So, (a – 1) / (b – 1) = (2 – 1) / (4 – 1) = 1/3 …(2)

Thus, (1) ≠ (2)

Hence, the given statement “If ‘a’ and ‘b’ are in direct proportion, then (a – 1) and (b – 1) are also in direct proportion” is false.

9. A housemaid is paid Rs. 800 for 8 days. If she works for 25 days, how much will she get?

Solution:

According to the given question, we get the following:

Number of days	8	25
Income (in Rs)	800	x

Here, we have taken the unknown income to be “x”.

If the housemaid works for many days, her income will be more. Similarly, if she works for fewer days, she will get less income.

Hence, the number of days worked and income is directly proportional.

Therefore, we can write

8/800 = 25/x

1/100 = 25/x

Hence, x = 25(100)

x = 2500.

Therefore, if she works for 25 days, she will get Rs. 2500.

10. If a woman earns Rs. 805 per week, how much will she earn in 16 days?

Solution: Rs. 1840

As we know, 1 week = 7 days.

Thus, the income of a woman in 7 days = 805.

Hence, the income of a woman in 1 day = 805/7 = 115.

So, the income of a woman in 16 days = 16 × 115 = 1840.

Therefore, a woman will earn Rs. 1840 in 16 days.

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Practice Questions

Solve the following direct proportion questions:

1. If the cost of 18 dolls is Rs. 630, how many dolls can be purchased for Rs. 455?

2. Find the missing values in the below-given table, if p is directly proportional to q.

p	4	9	___	___	3	___
q	16	___	48	36	___	4

3. Fill in the blanks in each of the given statements, such that the statement becomes true.

If x = 3y, then x and y vary ___ with each other.
If “a” and “b” are said to vary directly with each other, then ____ = k, where “k” is a positive number.

4. Rahul purchased 12 books for Rs. 156. Then find the cost of 7 such books.

5. If 2 kg sugar contains 7 × 10⁶ crystals, then find how many sugar crystals are present in 4 kg of sugar?

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