# Direct and Inverse Proportion Worksheets for Class 8

Download free pdf of Direct and Inverse Proportion Worksheets with answers for Class 8. Students can easily get all the Class 8 Maths Worksheets and Exercises in Free Printable ( PDF Format) as per the latest syllabus and examination pattern in CBSE and NCERT pattern. Below you will find all the Direct and Inverse Proportion related sums that are asked in 8th Grade Mathematics Exams Across Indian Schools.

## Direct and Inverse Proportion Worksheets for Class 8 in PDF Format

### Class 8 Direct and Inverse Proportion Worksheet with answers

Q.1 If x and y varies inversely as each other and x=2 when y=40. Find x when x=20.
(a) 40
(b) 16
(c) 4
(d) none of these

Solution :

To solve this, we can set up the proportion: (x₁ / y₁) = (x₂ / y₂)

(4 / 16) = (9 / y₂)

Cross-multiply: 4y₂ = 16 * 9

Now, solve for y₂: y₂ = (16 * 9) / 4 = 36

Answer: So, y when x = 9 is 36.

Q.2 If x and y varies inversely as each other and x=8 when y=10. Find y when x=5.
(a) 40
(b) 16
(c) 4
(d) none of these

Solution :

Using the same formula as above, we have: (4 / 16) = (12 / y₃)

Cross-multiply: 4y₃ = 16 * 12

Now, solve for y₃: y₃ = (16 * 12) / 4 = 48

Answer: So, y when x = 12 is 48.

Q.3 If a and b varies inversely as each other and a=16 when b=4.Find b when a=32.
(a) 2
(b) 8
(c) 4
(d) none of these

Solution:

Using the same formula: (4 / 16) = (1 / y₄)

Cross-multiply: 4y₄ = 16 * 1

Now, solve for y₄: y₄ = (16 * 1) / 4 = 4

Answer: So, y when x = 1 is 4.

Q.4 If a and b varies inversely as each other and a=16 when b=4. Find b when a=8.
(a) 2
(b) 8
(c) 4
(d) none of these

Solution:

Using the same formula: (4 / 16) = (3 / y₅)

Cross-multiply: 4y₅ = 16 * 3

Now, solve for y₅: y₅ = (16 * 3) / 4 = 12

Answer: So, y when x = 3 is 12.

Q.5 If x and y varies directly as each other and x=4 when y=16. Find y when x=9.
(a) 48
(b) 36
(c) 4
(d) none of these

Solution:

If x and y vary inversely as each other and x = 2 when y = 40, find x when x = 20.

In this case, we use the formula for inverse variation: x₁ * y₁ = x₂ * y₂

(2 * 40) = (20 * y₆)

Now, solve for y₆: y₆ = (2 * 40) / 20 = 4

Answer: So, x when y = 20 is 4.

Q.6 If x and y varies directly as each other and x=4 when y=16. Find y when x=12.
(a) 48
(b) 36
(c) 4
(d) none of these

Solution:

If x and y vary inversely as each other and x = 8 when y = 10, find y when x = 5.
Using the same formula:
(8 * 10) = (5 * y₇)

Now, solve for y₇:
y₇ = (8 * 10) / 5 = 16

Answer: So, y when x = 5 is 16.

Q.7 If x and y varies directly as each other and x=4 when y=16. Find y when x=1.
(a) 48
(b) 36
(c) 4
(d) none of these

Solution:

If a and b vary inversely as each other and a = 16 when b = 4, find b when a = 32.
Using the same formula:
(16 * 4) = (32 * b₁)

Now, solve for b₁:
b₁ = (16 * 4) / 32 = 2

Answer: So, b when a = 32 is 2.

Q.8 If x and y varies directly as each other and x=4 when y=16. Find y when x=3.
(a) 48
(b) 36
(c) 4
(d) none of these

Solution:

If a and b vary inversely as each other and a = 16 when b = 4, find b when a = 8.
Using the same formula:
(16 * 4) = (8 * b₂)

Now, solve for b₂:
b₂ = (16 * 4) / 8 = 32 / 8 = 4

Answer: So, b when a = 8 is 4.

Q.9 If 36 men can do a piece of work in 25 days, in how many days will 15 men do it?
(a) 60 days
(b) 75 days
(c) 50 days
(d) none of these

Solution:

If 36 men can do a piece of work in 25 days, in how many days will 15 men do it?
This is a direct proportion problem. We can set up a proportion:
(36 men / 15 men) = (25 days / x days)

Now, solve for x:
x = (36 * 25) / 15 = 60 days

Answer: So, 15 men will do it in 60 days.

Q.10 A work force of 50 men with a contractor an finish a piece of work in 5 months. In how many months the same work can be completed by 125 men?
(a) 2
(b) 8
(c) 4
(d) none of these

Solution:

A workforce of 50 men with a contractor can finish a piece of work in 5 months. In how many months can the same work be completed by 125 men?
This is a direct proportion problem. We can set up a proportion:
(50 men / 125 men) = (5 months / x months)

Now, solve for x:
x = (50 * 5) / 125 = 2 months

Answer: So, 125 men can complete the work in 2 months.

Q.11 A worker is paid Rs. 200 for 8 days work. If his total income of the month is Rs. 875, for how many days did he work?

Solution:

A worker is paid Rs. 200 for 8 days’ work. If his total income for the month is Rs. 875, for how many days did he work?
Let the number of days he worked be “x.”

We can set up a proportion:

(Income for x days / Income for 8 days) = (x / 8)

Rs. 200x / 8 = Rs. 875

Now, solve for x:

200x = 875 * 8
200x = 7000
x = 7000 / 200
x = 35 days

Answer: So, the worker worked for 35 days.

Q.12 If 52 men can do piece of work in 35days, in how many days 28 men will do it?

Solution:

If 52 men can do a piece of work in 35 days, in how many days will 28 men do it?
This is a direct proportion problem. We can set up a proportion:

(52 men / 28 men) = (35 days / x days)

Now, solve for x:

x = (52 * 35) / 28
x = 65 days

Answer: So, 28 men will do it in 65 days.

Q.13 If 56 men can do a piece of work in 42 days. How many men will do it in 14days?

Solution:

If 56 men can do a piece of work in 42 days, how many men will do it in 14 days?
This is an inverse proportion problem. We can set up a proportion:

(56 men * 42 days) = (x men * 14 days)

Now, solve for x:

(56 * 42) = (x * 14)
2352 = 14x

x = 2352 / 14
x = 168 men

Answer: So, 168 men will do it in 14 days.

Q.14 1200 men can finish a stock of food in 35 days. How many more men should join them so that the same stock may last for 25 days?

Solution:

1200 men can finish a stock of food in 35 days. How many more men should join them so that the same stock may last for 25 days?
This is a direct proportion problem. We can set up a proportion:

(1200 men / x men) = (35 days / 25 days)

Now, solve for x:

x = (1200 * 25) / 35
x = 857 men

Answer: So, 857 more men should join them.

Q.15 In a hostel of 50 girls there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?

Solution:

In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?
This is a direct proportion problem. We can set up a proportion:

(50 girls / 80 girls) = (40 days / x days)

Now, solve for x:

x = (50 * 40) / 80
x = 25 days

Answer: So, these provisions will last for 25 days.

Q.16 A group of 3 friends staying together consume 54kg of wheat every month. Some more friends join this group and they find that the same amount of wheat lasts for 18 days. How many new members are there in this group now?

Solution:

A group of 3 friends staying together consumes 54 kg of wheat every month. Some more friends join this group, and they find that the same amount of wheat lasts for 18 days. How many new members are there in this group now?
Let the number of new members be “x.”

We can set up a proportion:

(Initial consumption / New consumption) = (Initial days / New days)

(3 friends * 54 kg) / ((3 + x) friends * 18 days) = (1 month / (1/2) month)

Now, solve for x:

(3 * 54) / ((3 + x) * 18) = 2

(3 * 54) = 2 * (3 + x) * 18

162 = 36 * (3 + x)

162 = 108 + 36x

36x = 54

x = 54 / 36
x = 3

Answer: So, there are 3 new members in this group now.

Q.16 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?

Solution:

55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?
This is an inverse proportion problem. We can set up a proportion:

(55 cows * 16 days) = (x cows * 10 days)

Now, solve for x:

(55 * 16) = (10x)

880 = 10x

x = 880 / 10
x = 88 cows

Answer: So, 88 cows will graze the field in 10 days.

Q.17 Seema weaves 25 baskets in 35 days. In how many days will she weave 110 baskets?

Solution:

Three spraying machines working together can finish painting a house in 60 minutes. How long will it take for 5 machines of the same capacity to do the same job?
This is a direct proportion problem. We can set up a proportion:

(3 machines / 5 machines) = (60 minutes / x minutes)

Now, solve for x:

x = (3 * 60) / 5
x = 180 / 5
x = 36 minutes

Answer: So, it will take 36 minutes for 5 machines to finish painting the house.

Q.18 Three spraying machines working together can finish painting a house in 60 minutes. How long will it take for 5 machines of the same capacity to do the same job?

Solution:

If three spraying machines working together can finish painting a house in 60 minutes, we can find out how long it will take for 5 machines of the same capacity to do the same job by setting up a proportion:

(3 machines / 5 machines) = (60 minutes / x minutes)

Now, solve for x:

x = (3 * 60) / 5
x = 180 / 5
x = 36 minutes

Answer: So, it will take 36 minutes for 5 machines of the same capacity to finish painting the house.