Direct Proportionality

Q.

How to find the breadth of a rectangle if length and perimeter are given.

Q. If speed is constant, then distance and time are in proportion.

1. direct
2. inverse
3. continued

Q.

Question 1(e)

Determine if the following are in proportion:

4, 6, 8, 12

Q.

If two quantities have different units, then we can compare them by using the method of ratio.

1. Ratio

2. Proportion

Q.

Divide

8√15 by 2√3

Q. A printing machine can print 250 newspapers in 2 hours and 5 minutes. How many newspapers will it print in total if it is operated for half an hour more?

1. 310 newspapers
2. 390 newspapers
3. 250 newspapers
4. 300 newspapers

Q.

If $∆ABC~∆DEF$, $AB=4cm$, $DE=6$, $EF=9cm$ and $FD=12cm$ , then find the perimeter of $∆ABC$.

Q.

Question 51

If x and y are in inverse proportion, then (x + 1) and (y + 1) are also in inverse proportion.

Q. $\text{If x and y vary directly,}$
$y_1=x_2=5\text{and}{y}_2=y_1+10,\text{then what is the value of}{x}_1?$

1. $2$
2. $\frac{1}{2}$
3. $\frac{5}{3}$
4. $\frac{5}{2}$

Q.

Three numbers are in continued proportion whose mean proportional is 12 and the sum of the remaining two numbers is 26, then find these numbers

Q. If 5 : 6 = x : 12, then what is the value of x?

1. 6
2. 16
3. 22
4. 10

Q.

The area of a triangle is equal to that of square of side $60cm$. Find the side of a triangle whose corresponding altitude is $90cm$.

Q.

Question 54

When two quantities are related in such a manner that, if one increases, the other also increases, then they always vary directly.

Q.

If 9, x, x and 25 are in proportion, find the value of x.

1. 9

2. 12

3. 15

4. 18

Q.

The width of a rectangle is $8\mathrm{cm}$. If the length of the rectangle is twice the width, find its perimeter.

Q.

A wide screen television measures $36$ inches by $54$ inches. A movie theater screen measures $42$ feet by $63$ feet. Are the screen similars? Explain.

Q.

Question 126

Fill in the blank to make the statement true.

10001 x 0 = .............

Q.

If two quantities $x$ and$y$ vary directly with each other, then ______ of their corresponding values remains constant.

Q. If 10 : 5 = 20 : 10, then what is the constant of proportionality?

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

Q.

If a box of sweets is divided among 24 children, they will get 5 sweets each. If the number of the children is reduced by 4, each child would get___sweets?

1. 6

2. 7

3. 5

4. 8

Q.

Question 38

Fill in the blanks to make the statements true.

If two ratios are equal, then they are in ___.

Q.

The number of pipes used to fill a drum will be _________ to the time taken to fill the drum.

1. not at all proportional
2. None of the above

3. directly proportional

4. inversely proportional

Q.

Consider a square of side 4 units. What is the ratio of the perimeter of the square to its area?

1. 4:1

2. 1:1

3. 1:4

4. 2:2

Q.

Question 4(c)

Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion:

2 kg : 80 kg and 25 g : 626 g

Q.

A picture is 60 cm wide and 1.8 m long. The ratio of its width to its perimeter in lowest form is

1. 1 : 2

2. 1 : 3

3. 1 : 4

4. 1 : 8

Q. If $\sqrt{5^n}=125$, then =

(a) 25

(b) $\frac{1}{125}$

(c) 625

(d) $\frac{1}{5}$

Q.

Question 23

State whether the given statements are true (T) or false (F).

20 g : 100 g = 1m : 500 cm

Q.

Evaluate 2.66666666...+0.999999999....=0.232323....

Q.

A boy types 180 words in 2 minutes. How many minutes would he take to type 900 words ?

1. 10 minutes

2. 15 minutes

3. 20 minutes

4. 25 minutes

Q.

Find $x$ in the the given proportion:

$33:44::66:x$