Ratio and Proportion

6 )

Three numbers are in the ratio 3:4:5. The sum of the largest and the smallest equals the sum of the second and 52. the smallest number is.

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Answer :

Let the numbers be 3x, 4x and 5x
Now according to question
5x+3x = 4x+52
⇒ 4x=52
⇒ x=13
∴ Smallest number=3x=3×13=39

7 )

If the square of the sum of two numbers is equal to 4 times of their product, then the ratio of these numbers is:

1:3

3:2

1:1

1:5

2:3

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Answer :

Let the numbers are x and y
Now according to question

(x+y)² = 4xy
⇒ x² + y²+2xy = 4xy
⇒ x² + y²-2xy=0
⇒ (x-y)² = 0
so, x=y
∴ x:y=1:1

8 )

The sum of two numbers is equal to 20 and their difference is 25. The ratio of the two numbers is.

2 : 1

9 : 1

9 : 4

9 : 7

5 : 9

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Answer :

20+25 : 20-25
=45 : 5
=9 : 1

9 )

If A and B are in the ratio 4:5 and the difference of their squares is 81, what is the value of A?

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Answer :

Let A=4x and B=5x
Now according to question
(5x)² – (4x)² = 81
⇒ 9x² =81
⇒ x² =81/9 = 9
⇒ x= 3
∴ A=4x=4×3=12

10 )

The ratio of two numbers is 3:4 and their LCM is 120. The sum of numbers is.

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Answer :

Let the numbers be 3x and 4x respectively.
LCM of 3x and 4x=12x
⇒ 12x=120

⇒ x=10
∴ Sum of the numbers=3x+4x=7x=7×10=70