# Ratio & Propotion II

Q1:

The LCM of two numbers is 84.The numbers are in the ratio 4:7.Then the smallest number is?

Ans:

Let the numbers are 4x, 7x

Then LCM = x X 4 X 7 = 84.

ie; 28x = 84

x = 3

Smallest number = 4x = 4 X 3 = 12

Q2:

Two numbers are in the ratio 3:4.If 6 is added to both numbers the ratio become 4:5.Then the biggest number is?

Ans:

Let the numbers are 3x, 4x

if 6 is added the numbers are 3x + 6, 4x + 6

ie; 3x + 6/4x + 6 = 4/5

5(3x + 6) = 4(4x + 6)

15x + 30 = 16x + 24

x = 6

The biggest number is 4x = 4 X 6 = 24

Q3:

Which number can be exactly divide in the ratio 2:3:6?

84              88                96                  100

Ans:

2 + 3 + 6 = 11

Here multiple of 11 is 88.

Q4:

Two numbers are in the ratio 6:11.If the first number is 42,find the second number?

Ans:

Let the numbers are 6x, 11x

Given the first number is 42

ie; 6x = 42

ie;   x = 7

So the second number is 11x = 11 X 7 = 77

Q5:

Two numbers are in the ratio 3:4.Their product of LCM and HCF is 432.Then the sum of the numbers is?

Ans:

Let the numbers are 3x, 4x

LCM X HCF = Product of numbers.

ie; 4x X 3x = 432

12 x2  =  432

x = 6

So the sum of numbers is 3x + 4x = 3 X 6 + 4 X 6

=18 + 24  = 42

Q6:

The ratio between the areas of two squares are in the ratio 4:9.Then ratio between their sides are?

Ans:

Let the sides of each square are a1 , a2.

Then ratio of areas can be denoted as a12 : a22  = 4:9

So  the ratio between sides a1 : a2 = 2 : 3

Q7:

The average age of father and son is 40 years.Ratio between their ages is 7:3.Then the age of father is?

Ans:

Let the ages are 7x , 3x

Then 7x + 3x /2 = 40

x + 3x =80

10x = 80

x = 8

Age of father is 7x = 7 X 8 = 56