**Samacheer Kalvi Class 7 Maths Term 1 Chapter 4 Direct and Inverse Proportion Solutions**

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students by providing Solutions for Samacheer Kalvi Class 7 Maths Term 1 chapter 4 Direct and Inverse Proportion. Here students can easily find all the solutions for Direct and Inverse Proportion Exercise 4.1, 4.2 and 4.3. Also here our Expert Maths Teacher’s solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 4 solutions. Here all the solutions are based on Tamil Nadu State Board latest syllabus.

**Direct and Inverse Proportion Exercise 4.1 Solutions :**

**Direct and Inverse Proportion Exercise 4.1 Solutions :**

**(1) Fill in the blanks :**

**(i) If the cost of 8 apples is ₹56 then the cost of 12 apples is** __

**(ii) If the weight of one fruit box is 3 1/2 kg, then the weight of 6 such boxes is** __

**(iii) A car travels 60 km with 3 liters of petrol. If the car has to cover the distance of 200 km, it requires** __** liters of petrol.**

**(iv) If the cost of 7 m cloth is ₹294, then the cost of 5 m of cloth is** __

**(v) If a machine in a cool drinks factory fills 600 bottles in 5 hrs, then it will fill** __** bottles in 3 hours.**

**Solution : **

(i) → ₹ 84

(ii) → 21 kg

(iii) → 10 litre

(iv) → Rs 210

(v) → 360 bottles

**(2) Say True or False : **

**(i) Distance travelled by a bus and time taken are in direct proportion.**

**(ii) Expenditure of a family to number of members of the family are in direct proportion.**

**(iii) Number of students in a hostel and consumption of food are not in direct proportion.**

**(iv) If Mallika walks 1 km in 20 minutes, then she can cover 3 km in 1 hour.**

**(v) If 12 men can dig a pond in 8 days, then 18 men can dig it in 6 days.**

**Solution : **

(i) → True

(ii) → True

(iii) → False

(iv) → True

(v) → False

**(3) A dozen bananas costs ` 20. What is the price of 48 bananas?**

**Solution : **

Given, a dozen bananas costs ₹20.

We know, 1 dozen = 12 therefore 4 dozen = 48

Thus, for 1 dozen bananas cost = ₹20

So, for 4 dozen bananas cost

= ₹(20×4)

= ₹80

Therefore, ₹80 is the price of 48 bananas.

**(4) A group of 21 students paid Rs 840 as the entry fee for a magic show. How many students entered the magic show if the total amount paid was Rs 1,680?**

**Solution : **

Given, fees of 21 students = ₹840

So, let x students of fees = ₹1680

Therefore,

x = 21 × 1680/840

= 42 students

Therefore, the total amount paid was ₹1,680 for 42 students entered the magic show.

**(5) A birthday party is arranged in third floor of a hotel. 120 people take 8 trips in a lift to go to the party hall. If 12 trips were made how many people would have attended the party?**

**Solution : **

As per the question,

for 8 trip of lift = 120 people reach party Hall

So, for 12 trip of lift = x people reach to party Hall

Therefore,

x = 12 * 120/8

= x = 180

Therefore, 12 trips of lift made 180 people would have attended the party.

**(6) The shadow of a pole with the height of 8 m is 6 m. If the shadow of another pole measured at the same time is 30m, find the height of the pole?**

**Solution : **

Since, the shadow of another pole measured at the same time is 30 m

Let x be height of another pole

Thus, height of pole 8m = shadow 6m

So, height of pole x m = shadow 30 m

Therefore,

x = 8 × 30/6

= 8 × 5

= 40 m

Therefore, height of another pole is 40 m

**(7) A postman can sort out 738 letters in 6 hours. How many letters can be sorted in 9 hours?**

**Solution : **

According to the question,

for 6 hours = 738 letters

So, for 9 hours = x letters

Therefore,

x = 9 × 738/6

= 6642/6

= 1107

Therefore, In 9 hours postman sort out 1107 letters.

**(8) If half a meter of cloth costs Rs 15. Find the cost of 8 1/3 meters of the same cloth.**

**Solution : **

Since, cost of 1/2m of cloth is ₹15.

Let, cost of 8 1/3 = 25/3 m of cloth is ₹x

Therefore, x = (15 × 25/3)/0.5

= (5 × 25) /0.5

= 125/0.5

= 1250/5

=250

Therefore, a cost of 8 1/3 = 25/3 m of cloth is ₹250

**(9) The weight of 72 books is 9kg. what is the weight of 40 such books?**

**Solution : **

The weight of 72 books is 9 kg

The weight of 1 book

= 9000/72

= 125 g

The weight of 40 such books

= 40 x 125

= 5000 g

= 5 kg.

∴ The weight of 40 such books is 5 kg.

**(10) Thamarai pays Rs 7500 as rent for 3 months. With the same rate how much does she have to pay for 1 year?**

**Solution : **

Thamarai pays ₹7500 as rent for 3 months.

We know, 1 year = 12 month

For 3 months rent = ₹7500

Thus, for 12 months = 1 year = ₹x

Therefore,

x = 12 × 7500/3

= 4 × 7500

= ₹30000

Therefore, Thamarai pays ₹30000 as rent for 1 year.

**(11) If 30 men can reap a field in 15 days, then in how many days can 20 men reap the same field?**

**Solution : **

Given, 30 men can reap a field in 15 days

Thus, for 30 men = 15 days

So, for 20 men = x days

Therefore,

x = 20 × 15/30

= 300/30

= 10

Therefore, 20 men can reap a field in 10 days.

**(12) Valli buys 10 pens for Rs 180 and Kamala buys 8 pens for Rs 96. Can you say who bought the pen cheaper?**

**Solution : **

Since, Valli cost of 10 pens = ₹ 180

Thus, cost of 1 pen

= 180/10

= ₹18

Also since, Kamala cost of 8 pens = ₹96

Thus, cost of 1 pen

= 96/8

= ₹12

Therefore, Kamla bought the pen cheaper.

**(13) A motorbike requires 2 litres of petrol to cover 100 kilometers. How many litres of petrol will be required to cover 250 kilometers?**

**Solution : **

A motorbike requires 2 litres of petrol to cover 100 kilometers.

Thus, for 2 litres = 100 km

So, for x litres = 250 km

Therefore,

x = 2 × 250/100

= 500/100

= 5 litres

Therefore, a motorbike requires 5 litres of petrol to cover 250 kilometers.

**Objective Type Question Solution : **

**(14) If the cost of 3 books is 90, then find the cost of 12 books**

**(i) 300**

**(ii) 320**

**(iii) 360**

**(iv) 400**

**Solution : **

Correct Option → (iii)

The cost of 12 books will be Rs 360

**(15) If Mani buys 5 kg of potatoes for 75 then he can buy __ kg of potatoes for 105**

**(i) 6**

**(ii) 7**

**(iii) 8**

**(iv) 5**

**Solution : **

Correct Option → (ii)

7 kg of potatoes for 105

**(16) 35 cycles were produced in 5 days by a company then ___ cycles will be produced in 21 days**

**(i) 150**

**(ii) 70**

**(iii) 100**

**(iv) 147**

**Solution : **

Correct Option → (iv)

35 cycles were produced in 5 days by a company then 147 cycles will be produced in 21 days.

**(17) An aircraft can accommodate 280 people in 2 trips. it can take _____ trips to take 1400 people**

**(i) 8**

**(ii) 10**

**(iii) 9**

**(iv) 12**

**Solution : **

Correct Option → (ii)

It can take 10 trips to take 1400 people.

**(18) Suppose 3 kg. of sugar is used to prepare sweets for 50 members, then ___ kg. of sugar is required for 150 members**

**(i) 9**

**(ii) 10**

**(iii) 15**

**(iv) 6**

**Solution : **

Correct Option → (i)

Then 9 kg. of sugar is required for 150 members.

**Direct and Inverse Proportion Exercise 4.2 Solutions :**

**Direct and Inverse Proportion Exercise 4.2 Solutions :**

**(1) Fill in the blanks : **

**(i) 16 taps can fill a petrol tank in 18 minutes. The time taken for 9 taps to fill the same tank will be** __** minutes.**

**(ii) If 40 workers can do a project work in 8 days, then** __** workers can do it in 4 days.**

**Solution : **

(i) → 80 workers

(ii) → 32 minutes

**(2) 6 pumps are required to fill a water sump in 1 hr 30 minutes. What will be the time taken to fill the sump if one pump is switched off?**

**Solution : **

Let x be the time taken to fill the sump. The decrease in number of pumps lead to the increase in time. (Therefore, both are in inverse proportion)

For inverse proportion x_{1}y_{1} = x_{2}y_{2}

Hence,

6 × 90 = 5 × x …. ( since 1 hr = 60 min)

540 = 5x

x = 540/5

x = 108 min = 1 hr 48 min.

Therefore, 5 pumps are required to fill a water sump in 1 hr 48 minutes.

**(3) A farmer has enough food for 144 ducks for 28 days. If he sells 32 ducks, how long will the food last?**

**Solution : **

Let x be the number of days. The decrease in number of ducks lead to the increase in days.

(Therefore, both are in inverse proportion)

For inverse proportion x_{1}y_{1} = x_{2}y_{2}

Thus, 28 × 144 = x × 112 …. ( since, 144 – 32 = 112)

x = 28 × 144/112

x = 36

Therefore, a farmer sells 32 ducks then food last 36 days long.

**(4) It takes 60 days for 10 machines to dig a hole. Assuming that all machines work at the same speed, how long will it take 30 machines to dig the same hole?**

**Solution : **

Let x days for 30 machine to dig a hole. The increase in number of machine lead to the decrease in days. (Therefore, both are in inverse proportion)

For inverse proportion x_{1}y_{1} = x_{2}y_{2}

Thus, 60 × 10 = x × 30

x = 600/30

= 20 days

Therefore, it takes 20 days for 30 machines to dig a hole.

**(5) Forty students stay in a hostel. They had food stock for 30 days. If the students are doubled then for how many days the stock will last?**

**Solution : **

Let x days for 80 students food stocks will last. The increase in number of students lead to

the decrease in days. (Therefore, both are in inverse proportion)

For inverse proportion x_{1}y_{1} = x_{2}y_{2}

Thus, 30 × 40 = x × 80

x = 30×40/80

= 1200/80

= 120/8

= 15

Therefore, 15 days for 80 students food stocks will last.

**(7) It takes 120 minutes to weed a garden with 6 gardeners If the same work is to be done in 30 minutes, how many more gardeners are needed?**

**Solution : **

Let, x gardeners weed a garden in 30 min. The decrease in time lead to the increase gardeners.

(Therefore, both are in inverse proportion)

For inverse proportion x_{1}y_{1} = x_{2}y_{2}

Thus, 6 × 120 = x × 30

x = 6 × 120 /30

x = 720/30

= 72/3

= 24

Now, 24 – 6 = 18

Therefore, 18 gardeners more to weed a garden in 30 min.

**(8) Neelaveni goes by bi-cycle to her school every day. Her average speed is 12 km/hr and she reaches school in 20 minutes. What is the increase in speed, if she reaches the school in 15 minutes?**

**Solution : **

Let x km/hr Neelaveni reaches the school in 15 minutes. The decrease in time lead to the increase speed. (Therefore, both are in inverse proportion)

For inverse proportion x_{1}y_{1} = x_{2}y_{2}

Thus, 12 × 20 = x × 15

240 = x × 15

x = 240/15

x = 16

Now, 16 – 12 = 4

Therefore, for 4 km/hr increase the speed for Neelaveni reaches the school in 15 minutes.

**(9) A toy company requires 36 machines to produce car toys in 54 days. How many machines would be required to produce the same number of car toys in 81 days?**

**Solution : **

Let, x machines to produce car toys in 81 days.

The increase in number of days lead to the decrease in machine. (Therefore, both are in inverse proportion)

For inverse proportion x1y1 = x2y2

Thus, 36 × 54 = x × 81

x = 36 × 54 /81

x = 1944/81

= x = 24

Therefore, 24 machines to produce car toys in 81 days.

**Objective Type Question Solutions : **

**(10) 12 cows can graze a field for 10 days. 20 cows can graze the same field for** __** days**

**(i) 15**

**(ii) 18**

**(iii) 6**

**(iv) 8**

**Solution : **

Correct Option → (iii)

20 cows can graze the same field for 6 days.

**(11) typists are employed to complete a work in 12 days. if two more typists are added, they will finish the same work in** ___** days**

**(i) 7**

**(ii) 8**

**(iii) 9**

**(iv) 10**

**Solution : **

Correct Option → (ii)

They will finish the same work in 8 days.

**Direct and Inverse Proportion Exercise 4.3 Solutions :**

**Direct and Inverse Proportion Exercise 4.3 Solutions :**

**(1) If the cost of 7kg of onions is Rs 84 find the following**

**(i) Weight of the onions bought for Rs 180**

**(ii) The cost of 3 kg of onions**

**Solution : **

(i) Given, the cost of 7 kg of onions is ₹ 84

Thus, for ₹84 = 7 kg onions

So, for ₹180 = x kg onions

Therefore , x = 7 × 180/84

x = 1260/84

x = 15 kg

Hence, 15 kg weight of the onions bought for ₹180.

(ii) Given, the cost of 7 kg of onions is ₹ 84

Thus, for 7 kg onions cost = ₹84

So, for 3 kg onions cost = ₹x

Therefore, x = 3 × 84/7

= 252/7

= 36

Therefore, the cost of 3 kg of onions is ₹ 36.

**(2) If C = kd, (i) what is the relation between C and d? (ii) find k when C = 30 and d = 6 (iii) find C, when d = 10**

**Solution : **

(i) The relation between C and d is direct promotion.

(ii) Given, C = 30 and d = 6

Since, C = kd

Thus, k = C/d

k = 30/6

k = 5

(iii) Given, d = 10

From (ii) k = 5

Since, C = kd

C = 5 × 10

C = 50

**(3) Every 3 months Tamilselvan deposits Rs 5000 as savings in his bank account. In how many years he can save Rs 1,50,000.**

**Solution : **

As per the above question,

For 3 months deposits savings = ₹5000

So, for x months deposits savings = ₹150000

Therefore,

= x = 3 × 150000/5000

= 3 × 30

= 90 months

We know, 1 year = 12 months

Thus, 90 months = 90/12

= 7 6/12

= 7 1/2 years

Therefore, 7 1/2 years he can save ₹1,50,000.

**(4) A printer, prints a book of 300 pages at the rate of 30 pages per minute. Then, how long will it take to print the same book if the speed of the printer is 25 pages per minute?**

**Solution : **

Given, a printer, prints a book of 300 pages at the rate of 30 pages per minute.

Therefore, required time for 300 pages as 30 pages per minute

= 300/30

= 10 min

Now, supposed to print the same book if the speed of the printer is 25 pages per minute

Therefore, required time for 300 pages 25 pages per minute

= 300/25

= 12 min.

**(5) If the cost of 6 cans of juice is Rs 210, then what will be the cost of 4 cans of juice?**

**Solution : **

Given, the cost of 6 cans of juice is ₹210.

Thus, cost 6 can = ₹210

So cost of 4 can = ₹x

Therefore,

x = 4 × 210/6

= 840/6

= ₹140

Hence, cost of 4 cans juice is ₹140.

**(6) x varies inversely as twice of y. Given that when y = 6, the value of x is 4. Find the value of x when y = 8. **

**Solution : **

Given, x varies inversely as twice of y.

Also, given that when y = 6, the value of x is 4.

To find value of x when y = 8

Thus, x1y1 = x2 y2

4 × 6 = x × 8

24 = x × 8

x = 24/8

x = 3

Hence, the value of x is 3 when y = 8.

**(7) A truck requires 108 liters of diesel for covering a distance of 594 km. How much diesel will be required to cover a distance of 1650 km?**

**Solution : **

Given, a truck requires 108 liters of diesel for covering a distance of 594 km.

Thus, for 108 liters = 594 km

So, x litre = 1650 km

Therefore, x = 1650 × 108/594

x = 1,78,200/594

x = 300

Hence, 300 litres diesel will be required to cover a distance of 1650 km.

**Challenge Problem Solutions : **

**Challenge Problem Solutions :**

**(8) If the cost of a dozen soaps is Rs 396, what will be the cost of 35 such soaps?**

**Solution : **

Given, the cost of a dozen soaps is ₹396.

We know, 1 dozen = 12

Thus, cost 12 soaps = ₹396

So, cost 35 soaps = ₹x

Therefore, x = 35 × 396/12

x = 35 × 33

x = 1155

Hence, the cost of 35 soaps is ₹1155

**(9) In a school, there is 7 period a day each of 45 minutes duration. How long each period is, if the school has 9 periods a day assuming the number of hours to be the same?**

**Solution : **

Let, x min duration for each periods in a day 9 period. The increase in number of period lead to decrease the time period. (Therefore, both are in inverse proportion)

For inverse proportion x1y1 = x2y2

Thus, 45 × 7 = x × 9

x = 45×7/9

x = 5 × 7

x = 35

Hence, in a school, there is 9 period a day each of 35 minutes duration.

**(10) Cost of 105 notebooks is Rs 2415. How many notebooks can be bought for Rs 1863?**

**Solution : **

Given, cost of 105 notebooks is ₹2415.

Thus, 105 notebooks = ₹2415

So, x notebooks = ₹1863

Therefore, x = 105 × 1863/2415

x = 1,95,615 /2415

x = 81

Hence, in ₹1863 bought 81 notebooks.

**(11) 10 farmers can plough a field in 21 days. Find the number of days reduced if 14 farmers ploughed the same field?**

**Solution : **

Let, x be the number of days for 14 farmers can plough a field.

The increase in number of farmers lead to decrease the in number of days. (Therefore, both are

in inverse proportion)

Hence, x1y1 = x2y2

Thus, 21 × 10 = x × 14

210 = x × 14

x = 210/14

x = 15

Hence, 14 farmers can plough a field in 15 days.

**Next Chapter Solution : **

*👉 Geometry*