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If 2, 3, 28 and x are in proportion then find the value of x.
  • a)
    42
  • b)
    28
  • c)
    56
  • d)
    14
Correct answer is option 'A'. Can you explain this answer?

Let present age of father be 7x and that of son is 2x
after 10 years, their ages will be 7x+10 and 2x+10 respectively
so ratio will be
(7x+10)/(2x+10) = 9/4
28x+40 = 18x+90
10x = 50
x = 5
so present age of father is 7x =
35 years
 

If x, 30,24 and 16 are in proportion then find the value of x.
  • a)
    45
  • b)
    60
  • c)
    15
  • d)
    80
Correct answer is option 'A'. Can you explain this answer?

Mahesh Chavan answered
Given: x, 30, 24, 16 are in proportion.

To find: The value of x.

Solution:

The given numbers are in proportion. This means that the ratio of any two consecutive numbers is equal to the ratio of the other two consecutive numbers.

Therefore, we can write:

x/30 = 24/16

Cross-multiplying, we get:

16x = 30 × 24

Simplifying, we get:

16x = 720

Dividing both sides by 16, we get:

x = 45

Therefore, the value of x is 45.

Hence, option A is the correct answer.

In a school, there were 73 holidays in one year. What is the ratio of the number of holidays to the number of days in one year?
  • a)
    it is 5:1
  • b)
    it is 1:5
  • c)
    it is 1:4
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Gayatri Chavan answered
Given:
Number of holidays in a year = 73.
To do:
We have to find the ratio of the number of holidays to the number of days in one year.
Solution:
Number of days in a year = 365.
Therefore,
The ratio of the number of holidays to the number of days in one year = 73:365 = 1:5.

If 9, 18, x and 8 are in proportion then find the value of x.
  • a)
    2
  • b)
    4
  • c)
    3
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Neha Mehta answered
Given: 9, 18, x, 8 are in proportion

To find: value of x

Solution:

We know that when four numbers are in proportion, the product of the extremes is equal to the product of the means.

So, we can write:

9 × 8 = 18 × x

72 = 18x

4 = x

Therefore, the value of x is 4.

Hence, option B is the correct answer.

Find the ratio of 81 to 108.
  • a)
    it is 1:4
  • b)
    it is 4:3
  • c)
    it is 3:4
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Saikat Rane answered
Ratio refers to the quantitative relationship between two amounts or values. It is expressed in the form of a:b, where a and b are the two values being compared.

To find the ratio of 81 to 108, we need to divide both numbers by their greatest common factor, which is 27.

81 ÷ 27 = 3
108 ÷ 27 = 4

Therefore, the ratio of 81 to 108 is 3:4.

Option C, "it is 3:4", is the correct answer.

Length of a room is 30 m and its breadth is 20 m. Find the ratio of length of the room to the breadth of the room.
  • a)
    it is 2:3
  • b)
    it is 3:2
  • c)
    it is 1:3
  • d)
    it is 1:2
Correct answer is option 'B'. Can you explain this answer?

Jay Goyal answered
To find the ratio of length to breadth, we need to divide the length of the room by the breadth of the room.

Given:
Length of the room = 30 m
Breadth of the room = 20 m

To find the ratio of length to breadth, we divide the length by the breadth:

Ratio = Length / Breadth

Let's calculate:

Ratio = 30 m / 20 m

Simplifying the division, we get:

Ratio = 3/2

Thus, the ratio of length to breadth is 3:2, which corresponds to option B.

Explanation:
The ratio of length to breadth represents the relationship between the length and breadth of the room. In this case, the length is 30 m and the breadth is 20 m. When we divide the length by the breadth, we get a ratio of 3/2. This means that for every 3 units of length, there are 2 units of breadth. So, the ratio of length to breadth is 3:2.

If 14, 16, x and 24 are in proportion then find the value of x.
  • a)
    10.5
  • b)
    21
  • c)
    5
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Praveen Kumar answered
To find the value of x in the proportion 14 : 16 = x : 24, use cross-multiplication:
14 × 24 = 16 × x
336 = 16x
Divide both sides by 16:
x = 21

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