Direct Variation

Q.

The cost of diamond varies directly as the square of its weight. A diamond weighting 10 decigrams costs Rs. 8, 000. If it breaks into two pieces whose weights are in the ratio 3:2, then the loss incurred (in rupees) is

1. 3960

2. 4040

3. 4160

4. 3840

Q. *A MAN travels 600km apart by train and partly by car. It takes 8 hours and 40 minutes if he travels 320 km by train and rest by car. It would take 30 minutes more if he travels 200 km by train and the rest by the car/. Find the speed of the train and by car separately

Q.

A ball falls vertically after being dropped. The ball falls a distance d metres in a time of t seconds. d is directly proportional to the square of t.
The ball falls 20 metres in a time of 2 seconds.
The time (in seconds) that the ball takes to fall 605 m is

1. 16

2. 14

3. 9

4. 11

Q.

Question 52

Three times a number is 200% increase in the number, then one-third of the same number is 200% decrease in the number.

Q. A train and a car start together from a point. The train's speed is 80 kmph and the car's speed is 60% of the train's speed. The train crosses a station in 15 minutes. How much distance will the car travel in the time the train takes to cross 3 stations? (Assume constant distance betweeen consecutive stations)

1. 45 km
2. 54 km
3. 48 km
4. 36 km

Q.

If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?

1. 100 days

2. 144 days

3. 160 days

4. 180 days

Q.

In the equation y = x + 3, y is directly proportional to x.

1. True

2. False

Q.

If 16 men can make 320 art pieces in one day, how many men will be needed to make 960 such art pieces in one day?

1. 48

2. 50

3. 40

4. 28

Q. If $x\propto yz$ and $y\propto zx$, then prove that $z$ is a non-zero variation constant.

Q.

Two positive numbers x and y are inversely proportional. If x increases by 20%, then percentage decrease in y is

1. 20

2. $16\frac{2}{3}$

3. 5

4. $1\frac{9}{11}$

Q.

The cost of diamond varies directly as the square of its weight. A diamond weighing10 decigrams cost Rs. 8, 000. If it breaks into two pieces whose weights are in the ratio 3: 2, then the loss incurred (in rupees) is

1. 4040

2. 4160

3. 3840

4. 3960

Q.

In a class of 100 students, 12 students drink only milk and 5 students drink only coffee and 8 students drink only tea. Other report says 30 students take both coffee and tea, 25 students take milk and tea and 20 students take only milk and coffee. 10 students drink all the three. Find the number of students who do not drink anything.

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Q.

Question 95

How much more percent seats were won by X as compared to Y in assembly election in the state based on the data given below?

$\begin{array}{c}\\ \text{Party}\text{Won(out of 294)}\\ X158\\ Y105\\ Z18\\ W13\end{array}$

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 Rs.19, then the cost of printing a book with 280 pages 22 lines on each page and 10 words in each line is

1. Rs. 14

2. Rs. 16

3. Rs. 18

4. Rs. 20

Q.

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?

1. 4 cm

2. 6 cm

3. 9 cm

4. 8.2 cm

Q.

If x ∝ y , y ∝ z and z ∝ x , then the product of the 3 non - zero variation constant is :

1. 0

2. xyz

3. 1

4. Can't be determined

Q.

Meenakshee cycles to her school at an average speed of 12 km/hr and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be:

1. $\frac{20}{3}$ km/hr

2. 16 km/hr

3. 20 km/hr

4. 15 km/hr

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 Rs.19, then the cost of printing a book with 280 pages 22 lines on each page and 10 words in each line is

1. Rs. 14

2. Rs. 16

3. Rs. 18

4. Rs. 20

Q. Arya is a writer. Today, he has a target to write 60 pages of a story. So, he starts writing early at 9 a.m. He writes 4 pages in an hour. At around 1 p.m., he increases his speed and starts writing 11 pages in an hour.
Find the total time Arya takes to complete the story.

1. 15 hours
2. 10 hours
3. 8 hours
4. 6 hours

Q.

$$\begin{array}{cccc}X& 90& 180& 150\\ Y& 20& 10& 5\end{array}$$

From the above given table, we can say that X and Y are inversely proportional.

1. True

2. False

Q. Given X is directly proportional to Y. Fill the missing values of a and b.

1. 9
2. 12
3. 45
4. 50

Q.

A car travels a distance of 225 km using 25 litres of petrol. How many litres of petrol will be required to cover a distance of 540 kilometres by this car?

1. 41 L

2. 49 L

3. 58 L

4. 60 L

Q.

Bella cycles to her school at an average speed of 12 km/hr and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be:

1. $\frac{20}{3}$ km/hr

2. 16 km/hr

3. 20 km/hr

4. 15 km/hr

Q.

Two positive numbers x and y are inversely proportional. If x increases by 20%, then percentage decrease in y is

1. 20

2. $16\frac{2}{3}$

3. 5

4. $1\frac{9}{11}$

Q. In which of the following situations do the list of numbers involved form an A.P.?
Give reasons for your answers.
The number of bacteria in a certain food item after each second, when they double in every second.

Q.

In a town of 10, 000 families it was found that $40\%$ family buy newspaper A, $20\%$ buy newspaper B and $10\%$ families buy newspaper C, $5\%$ families buy A and B, $3\%$ buy B and C, and $4\%$ buy A and C. If $2\%$ families buy all the three newspapers, then number of families which buy A only is

1. 3100

2. 3300

3. 2900

4. 1400

Q.

Meenakshee cycles to her school at an average speed of 12 km/hr and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be:

1. $\frac{20}{3}$ km/hr

2. 16 km/hr

3. 20 km/hr

4. 15 km/hr

Q.

The cost of diamond varies directly as the square of its weight. A diamond weighting 10 decigrams costs Rs. 8, 000. If it breaks into two pieces whose weights are in the ratio 3 : 2, then the loss incurred (in rupees) is

1. 3960

2. 3840

3. 4040

4. 4160

Q.

If two quantities a and b are in direct variation, then the ratio $\frac{a}{b}$ is always:

1. constant

2. greater than 1

3. equal to 1

4. None of these

Q.

At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?

1. 7.2 m

2. 9.0 m

3. 10.2 m

4. 9.6 m