Application of Direct Proportionality

Q.

The mass of oxygen and hydrogen in any sample of water is approximately in the ratio 8:1, how many grams of hydrogen would you find in 1 kg of water?

1. 111.1 grams

2. 888.8 grams

3. 0.111 grams

4. 0.888 grams

Q.

Two natural numbers are in the ratio 3:4. The sum of their squares is 625. Find the numbers.

1. 20, 10

2. 15, 20

3. 5, 10

4. 15, 10

Q.

The ratio of storybooks to other books in a library is $2:7$. If the total number of story books is $400$, then find the total number of books in the library.

Q.

Question 16

Both x and y vary directly with each other and when x is 10, y is 14, which of the following is not a possible pair of corresponding values of x and y?
(a) 25 amd 35
(b) 35 and 25
(c) 35 and 49
(d) 15 and 21

Q. At a certain time of day , a man 6 feet tall casts his shadow 8 feet long . Find the length of shadow cast by a building 45 feet tall , at the same time.

Q.

Question 77 (iii)

From the following table determine if x and y are in direct proportion or not.

Q.

The ratio of chocolates to ice cream cones in a box is 2:5. If there are 10 chocolates in the box, find the number of ice cream cones in it.

1. 15

2. 10

3. 20

4. 25

Q. If price of 10 gram gold is ₹30000, then match the following weight of gold with corresponding prices.

1. ₹15000
2. 9.3 gram
3. 14.7 gram
4. ₹54000

Q.

The ratio of the number of girls to that of boys in a school is $9:11$.If the number of boys in the school is $2035$, find:

The number of students in the school

Q.

In all the paper sizes A0, A1, A2, etc, the ratio of the length of the longer side to that of the shorter side is

1. √2 : 1

2. 1 : √2

3. √3 : 1

4. 1:2

Q.

We have a map with a scale of 1:50000000. How much would 1cm measure in actual distance?

1. 1.6 km

2. 1 km

3. 8 km

4. 0.8 km

Q.

Everyday Rohan rides his bicycle as part of his exercise. While travelling at a constant rate, he rides 5 miles in 25 minutes. At this rate , how long would it take Rohan to cycle 10 miles ?

1. 25 minutes

2. 30 minutes

3. 15 minutes

4. 50 minutes

Q.

In a mixture of 42 litres, the ratio of sugar solution to salt solution is 3:4. Find the amount of sugar solution to be added to convert the ratio to 4 :3.

1. 10 litres

2. 7 litres

3. 14 litres

4. 20 litres

Q.

Find $x$ if $\frac{8x^3+6x}{12x^2+1}=\frac{35}{19}$

1. 2.5

2. 4.5

3. 10

4. 6

Q. A sack contains 3 packs of sugar and each pack contains 2 kg of sugar. In 12 sacks, what will be the weight of sugar present?

1. 48 kg
2. 36 kg
3. 72 kg
4. 48 kg

Q. The length of a cuboid is twice its breadth.The breadth is twice its height.Find the ratio of the lateral surface area to the total surface area of the cuboid.Given that the height of the cuboid is 2 cm

Q.

Question 77 (i)

From the following table determine if x and y are in direct proportion or not

Q. If a tree of height 12 m casts a shadow of 30 m, then a tree of height 16 m will cast a shadow of .

1. 32 m
2. 35 m
3. 40 m
4. 45 m

Q. Area of an equilateral triangle is in proportion with square of its sides.

1. direct
2. continued
3. inverse

Q.

You are giving a patient $3cc/min$ of a given solution intravenously. If this continues for $24$ hours, how many liters of this solution will you need?

Q.

The number of workers for a job and the time needed to complete the job

1. is a case of direct proportion.

2. is a case of indirect proportion.

3. Data insufficient

4. Not proportionate

Q.

Arrange the following steps of an experiment in sequential order to show that the body moves with uniform velocity.

1. Take a long thread and tie one end of it to a trolley and the other end of it to the second hand of a clock.
2. Spread a sheet of white paper on a horizontal table.
3. Arrange a trolley with an ink dropper attached to it.
4. Place the whole arrangement on the table.
5. Measure the distance between successive drops and note the time intervals between the drops.
6. When the trolley driven by the clock moves forward, ink drops fall on the paper at regular intervals.
7. Calculate the ratio of the distance between the successive drops to the time and it is observed that the ratio remains constant.

1. B C E F A D G

2. A B C E G F D

3. A C B D F G E

4. B C A D F E G

Q.

A fire burns steadily for 3 hours with 6 logs of wood. How many hours will it burn if 12 logs are used?

1. 2 hours

2. 4 hours

3. 6 hours

4. 8 hours

Q.

Raghu travelled 30 km by car in 2 litres of petrol. How many litres of petrol is required to travel 150 km?

1. 15 litres

2. 20 litres

3. 10 litres

4. 5 litres

Q. If $\frac{a}{3}=\frac{b}{7}=\frac{4a+5b}{Q}$. Find the value of Q?

Q. We have a map with a scale of 1:50000000. How much would 1 cm measure in actual distance?

1. 400 km
2. 320 km
3. 200 km
4. 500 km

Q.

If u:v = 2:3, find the ratio 15u + 12v : 20u + 16v

1. 1:4

2. 3:4

3. 4:3

4. 6:5

Q.

In a year, Seema earns Rs 1, 50, 000 and saves Rs 50, 000. Find the ratio of

(a) Money that Seema earns to the money she saves.

(b) Money that she saves to the money she spends.

Q. Price of petrol is ₹78 per litre, then match the following prices with volumes of petrol.

1. ₹171.60
2. 1.67 litre
3. ₹304.20
4. 1.3 litre

Q.

Question 77 (ii)

From the following table x and y are in direct proportion.

1. x and y are in direct proportion.

2. x and y are not in direct proportion.