Direct Variation

Q. For direct variation the value of $k$ can be either positive or negative.

1. True
2. False

Q.

If 4 dozen eggs cost ₹ 144, find the cost of 5 scores of eggs [1 score = 20]

1. 450

2. 300

3. 360

4. 250

Q. A bus travels 40 km in 30 minutes. If the speed of the bus remains the same, how far can it travel in 3 hours?

1. 220 kms
2. 240 kms
3. 200 kms
4. 250 kms

Q.

Reenu types 540 words during half an hour. How many words Would she type in 8 minutes ?

Q. X varies directly as the square of Y. If X = 1 when Y = 2, then find the constant of variation.

1. 0.25
2. 0.3
3. 0.5
4. 0.75

Q. X varies directly as the cube of Y. If X = 3 when Y = 2, then find the constant of variation.

1. 0.375
2. 0.25
3. 0.2
4. 0.5

Q. A varies directly as the square of B. If A = 48 when B = 4, then find the constant of variation.

1. 1
2. 2
3. 3
4. 4

Q. The expenditure of a family is directly proportional to the number of members in the family. If the expenditure of a family is ₹ 10, 000 when there are 5 members, then find the expenditure when there are 10 members in the family.

1. ₹ 30, 000
2. ₹ 20, 000
3. ₹ 15, 000
4. ₹ 10, 000

Q. If 4 tea-spoons of sugar is added in 2 cups of tea, then how many tea-spoons are required for 4 cups of tea?

1. 8 tea-spoons
2. 5 tea-spoons
3. 6 tea-spoons
4. 10 tea-spoons

Q. y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation.

1. k = 9
2. k = 5
3. k = 3
4. k = 6

Q.

Check whether the given ratios are equal i.e., they are in proportion. If yes, then write them in the proper form $1:5\mathrm{and}3:15$.

Q. The model of a chip is scaled at 50:1. If the length of the model of the microchip is 0.5 mm, then how many microchips can be arranged in a line on a 1 m long board?

1. 60
2. 50
3. 45
4. 40

Q.

Reema weaves $35$ baskets in $25$ days. In how many days will she weave $55$ baskets?​

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Q. Cost of groundnuts is directly proportional to its weight. If cost of 5 kg groundnuts is 450 then find the cost of 100 kg.

1. 9000
2. 5000
3. 4500
4. 4000

Q. The efficiency of a machine is directly proportional to the number of units produced. If the efficiency of the machine is 125 % when 25 units are produced, then find the efficiency of the machine when 10 units are produced .

1. 100 %
2. 50 %
3. 75 %
4. 150 %

Q.

If the cost of printing a book of 380 pages with 20 lines on each page and on an average 11 words in each line is ₹ 19, then the cost of printing a book with 280 pages 22 lines on each page and 10 words in each line is

1. ₹ 14

2. ₹ 16

3. ₹ 18

4. ₹ 20

Q. Find the missing entry:

Quantity	1	3	5	7
Price	50	150	250	__

1. 200
2. 450
3. 300
4. 350

Q. X varies directly as Y. If X = 5 when Y = 25, then find the constant of variation.

1. 0.2
2. 0.25
3. 0.5
4. 0.75

Q. Two numbers are in the ratio $4:7$. If their L.C.M is $168$, find the numbers.​

Q.

Question 93

Ms Anita has to drive from Jhareda to Ganwari. She measures a distance of 3.5 cm betweeen these village on the map. What is the actual distance between the villages, if the map scale is 1 cm= 10 km?

Q. The cost of production is directly proportional to the number of units produced. If the cost of production is ₹ 5, 000 when 25 units are produced, then find the cost of production when 100 units are produced .

1. ₹ 20, 000
2. ₹ 7, 500
3. ₹ 2, 500
4. ₹ 10, 000

Q.

Question 08.
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

Q.

Question 29

On increasing a, b increases in such a manner that $\frac{a}{b}$ remians___and postive, then a and b are said to vary directly with each other.

Q. A workforce of 210 men with a supervisor can finish a certain piece of work in 5 months. How many extra men must he employ if he want to complete job in just 2 months?
[2 marks]

Q.

Question 43

Two quantities x and y are said to vary directly with each other if for some rational number k, xy =k.

Q. The pressure of a vessel is directly proportional to the cube of its volume. If the pressure of the vessel is 125 Bar when the volume of the vessel is 5 Litres.Find the pressure when the volume of the vessel is 2 Litres.

1. 8 Bar
2. 5 Bar
3. 16 Bar
4. 22 Bar

Q. If 11 printers can print 22 pages in a second, then find the number of pages printed by 5 such printers in a second.

1. 10 pages
2. 12 pages
3. 16 pages
4. 20 pages

Q. The pressure of a vessel is directly proportional to the square of its volume. If the pressure of the vessel is 5 Bar when the volume of the vessel is 2 Litres.Find the pressure when the volume of the vessel is 1 Litre.

1. 1.25 Bar
2. 6.25 Bar
3. 5 Bar
4. 0.25 Bar

Q. For direct variation can the value of $k$ be either positive or negative?

1. Yes
2. No

Q. If 10 printers can print 50 pages in a second, then find the number of pages printed by 2 such printers in a second.

1. 6 pages
2. 8 pages
3. 10 pages
4. 12 pages