CG SCERT (Chhattisgarh Board) Class 8 Mathematics Solutions | 2026-27 Official Edition
Complete 100% textbook-grounded CG Board Class 8 Mathematics Chapter 7 Solutions: Direct and Inverse Variation (अनुक्रमानुपाती एवं व्युत्क्रमानुपाती विचरण) in Bilingual Format (English & Hindi Medium).
Question 1
In the following tables are x and y…
निम्नलिखित तालिकाओं में क्या x और y अनुक्रमानुपाती…
📝 Question:
In the following tables, are x and y in direct variation? Find the value of the constant ratio also. Table I:* x =, y =
💡 Solution:
Since the ratio x/y is constant for all values, x and y are in direct variation. Constant ratio k = 1/3.
Direct variation
- Table II: x = [2.5, 7.5, 11, 17.5, 19], y = [2.5, 7.5, 11, 17.5, 19]
Since the ratio is constant, x and y are in direct variation. Constant ratio k = 1.
Direct variation
- Table III: x =, y =
The ratio x/y is not constant. Therefore, x and y are not in direct variation.
It's not a direct variation
- Table IV: x =, y = [2, 1, 2/3, 1/2, 2/5]
The ratio x/y is not constant. Therefore, x and y are not in direct variation.
It's not a direct variation
Question 2
Fill in the blanks in the following direct…
Fill in the blanks in the following direct…
📝 Question:
Fill in the blanks in the following direct variation table:** x: 1, 2, , 4, 5, y: 50, , 150, 200, , 300
💡 Solution:
100, 3, 250, 6
Question 3
In the following table x y are in…
In the following table x y are in…
📝 Question:
In the following table, x & y are in direct variation. Find the value of constant ratio k.** x =, y =
💡 Solution:
k = x/y = 2/14 = 4/28 = 8/56 = 16/112 = 32/224 = 1/7
k = 1/7
Question 4
A car runs 600 km in 3 hours…
एक कार 3 घंटे में 600 किमी चलती…
📝 Question:
A car runs 600 km in 3 hours. How far will it travel in 5 hours?
💡 Solution:
1000 Km
Question 5
Which of the following quantities are in direct…
निम्नलिखित में से कौनसी राशियाँ अनुक्रमानुपाती विचरण में…
📝 Question:
Which of the following quantities are in direct variation?
💡 Solution:
(i) Number of objects and their prices.**
(ii) Number of Mathematics books of class 7th and their prices.
(iii) Area of a field and its price.
(iv) Quantity of milk (in lt.) and its price.
(v) Number of labourers and the total number of days in which the work is completed.
(vi) Speed and time when the distance travelled remains the same.
- (i), (ii), (iii), (iv) are in direct variation because increasing one quantity increases the other in the same ratio.
(i), (ii), (iii), (iv)
Question 6
Price of 15 tickets of equal price is…
समान मूल्य के 15 टिकटों का मूल्य रु…
📝 Question:
Price of 15 tickets (of equal price) is Rs. 18. How many tickets of the same price can be bought for Rs. 72?
💡 Solution:
60 ticket
Question 7
A car covers 432 km in 48 lt…
एक कार 48 लीटर पेट्रोल में 432 किमी…
📝 Question:
A car covers 432 km in 48 lt of petrol. What distance will it travel in 20 lt of petrol?
💡 Solution:
180 Km
Question 8
The cost of 2 dozen oranges is Rs…
2 दर्जन संतरों का मूल्य रु 48 है।…
📝 Question:
The cost of 2 dozen oranges is Rs. 48. Find the cost of 108 oranges
💡 Solution:
Rs. 216
Question 9
A machine prints 200 pages in 5 min…
एक मशीन 5 मिनट में 200 पृष्ठ छाप…
📝 Question:
A machine prints 200 pages in 5 min. How much time will it take to print 2 × 103 pages?
💡 Solution:
50 minute
Question 10
A cyclist covers 12 km in 3 hours…
एक साइकल सवार 3 घंटे में 12 किमी…
📝 Question:
A cyclist covers 12 km in 3 hours. How much time will be taken by him to cover 20 km?
💡 Solution:
5 hours
Question 11
The wages of 25 labourers is Rs 1250…
25 मजदूरों की मजदूरी रु 1250 है। 40…
📝 Question:
The wages of 25 labourers is Rs. 1250. What is the amount of wages for 40 labourers?
💡 Solution:
Rs. 2000
Question 12
A labourer gets Rs 806 for working 13…
एक मजदूर को 13 दिन काम करने पर…
📝 Question:
A labourer gets Rs. 806 for working 13 days. How many days would he have worked if he was paid Rs. 1798?
💡 Solution:
29 days
Question 13
Namrata takes 1225 steps to cover a distance…
नम्रता 100 मीटर चलने में 1225 कदम चलती…
📝 Question:
Namrata takes 1225 steps to cover a distance of 100 m. How much distance will she cover in 2835 steps?
💡 Solution:
- Let distance covered be x metres.
- By Direct Variation / :
(1225)/(100) = (2835)/(x)
x = (2835 × 100)/(1225) = (283500)/(1225) = 231.43 m
Question 14
A dealer gets a commission of Rs 73…
एक डीलर को रु 1000 का सामान बेचने…
📝 Question:
A dealer gets a commission of Rs. 73 for selling items worth Rs. 1000. How much commission will he get on selling items of Rs. 100?
💡 Solution:
Rs. 7.30
Question 15
The thickness of 500 sheets of paper is…
कागज की 500 शीटों की मोटाई 35 सेमी…
📝 Question:
The thickness of 500 sheets of paper is 3.5 cm, find the thickness of 275 sheets
💡 Solution:
1.925 cm
Question 16
A man can read 180 words in 1…
एक व्यक्ति 1 मिनट में 180 शब्द पढ़…
📝 Question:
A man can read 180 words in 1 min. How much time will it take him to read 768 words?
💡 Solution:
4 4/15 minute or 256 seconds
Question 17
Sunita types 1080 words in 1 hour Find…
सुनीता 1 घंटे में 1080 शब्द टाइप करती…
📝 Question:
Sunita types 1080 words in 1 hour. Find her rate of typing per minute
💡 Solution:
18 words per minute
Question 18
25 labourers make a 75 km long road…
25 मजदूर एक सप्ताह में 75 किमी लंबी…
📝 Question:
25 labourers make a 7.5 km long road in one week. How many labourers will make a road of 10.2 km in 1 week?
💡 Solution:
34 labours
Question 1
If x and y are in inverse ratio…
If x and y are in inverse ratio…
📝 Question:
If x and y are in inverse ratio, fill in the table appropriately:** x: 8, 6, 4, , 36 y: 9, 12, , 10,
💡 Solution:
x =, y =
Question 2
Fill in the blanks in variation table Speed…
Fill in the blanks in variation table Speed…
📝 Question:
Fill in the blanks in variation table:** Speed (in km/hr): 4, 8, , , 64 Time taken (in min): , 40, 20, 10,
💡 Solution:
Speed: 4, 8, 16, 32, 64; Time: 80, 40, 20, 10, 5
Question 3
10 labours finish a task in 2 days…
10 मजदूर किसी काम को 2 दिन में…
📝 Question:
10 labours finish a task in 2 days. How many days will 2 labours take to finish the same task?
💡 Solution:
10 day
Question 4
45 labours finish the work in 27 days…
45 मजदूर किसी काम को 27 दिन में…
📝 Question:
45 labours finish the work in 27 days. How many labourers will complete the same work in 15 days?
💡 Solution:
81 day (labourers)
Question 5
A bus takes 6 hours to cover a…
एक बस 30 किमीघंटा की चाल से एक…
📝 Question:
A bus takes 6 hours to cover a certain distance with a speed of 30 km/hr. What speed should the bus have to cover the same distance in 4 hours?
💡 Solution:
45 Km/hr
Question 6
40 horses eat 1 quintal of grain in…
40 घोड़े 1 क्विंटल अनाज 7 दिन में…
📝 Question:
40 horses eat 1 quintal of grain in 7 days. How many horses will eat the same quantity of grain in 28 days?
💡 Solution:
10 horses
Question 7
A hostel has 15 days of food for…
एक छात्रवास में 300 छात्रों के लिए 15…
📝 Question:
A hostel has 15 days of food for 300 students. If 200 students leave the hostel due to vacations, then for how many days will the food last?
💡 Solution:
45 day
Question 8
A military camp has 25 days of food…
एक सैन्य शिविर में 700 सैनिकों के लिए…
📝 Question:
A military camp has 25 days of food for 700 soldiers. Due to the arrival of some more soldiers, the food finishes in 20 days. Find the number of new soldiers that arrived in the camp
💡 Solution:
175 soldier
Question 9
A man completes a book in 15 days…
एक व्यक्ति प्रतिदिन 8 पृष्ठ पढ़कर 15 दिन…
📝 Question:
A man completes a book in 15 days by reading 8 pages per day. If he reads 12 pages daily, then how many days will he take to finish the book?
💡 Solution:
10 day
Question 10
A military camp has 21 days of ration…
एक सैन्य शिविर में 105 सैनिकों के लिए…
📝 Question:
A military camp has 21 days of ration for 105 soldiers. If 42 more soldiers arrive in the camp, then how many days will the ration last?
💡 Solution:
15 day
Question 11
Which are in inverse variation in the following…
निम्नलिखित में से कौन व्युत्क्रमानुपाती विचरण में हैं
📝 Question:
Which are in inverse variation in the following?* (i) Number of books bought and the cost of each book. (ii) Distance traveled by the bus and the cost of petrol consumed. (iii) Time taken by a cycle to cover a fixed distance with its speed. (iv) The number of men employed to make a bridge and the time taken to make the bridge. (v) Number of students and the weight of sweets distributed among them if 40 kg sweets are to be distributed. (vi) Wages and hours of work. (vii) Number of objects and their total price
💡 Solution:
(iii), (iv), (v)** are in inverse variation because increasing one variable decreases the other proportionally.
(iii), (iv), (v)
Question 12
On 26th January 100 gm sweets are distributed…
26 जनवरी पर 800 छात्रों में प्रति छात्र…
📝 Question:
On 26th January, 100 gm sweets are distributed per student among 800 students. If the same amount of sweets is to be distributed among 1000 students, how many grams of sweets will each student get?
💡 Solution:
80 gm
Question 13
If a tap takes 1 hr in filling…
यदि एक नल 1 घंटे में 640 लीटर…
📝 Question:
If a tap takes 1 hr in filling 640 lt water, then a water tank is filled in 10 hours. If the same tank was filled by another tap in 8 hours, how many liters will be filled in 1 hour by this tap?
💡 Solution:
800 litre