Question

A bag contains some number of white balls, twice the number of white balls are blue balls, thrice the number of blue balls are the red balls. If the total number of balls in the bag are 27 Then calculate the number of balls of each colour present in the bag​

Answer 1

Given :-

• A bag contains some number of white balls, twice the number of white balls are blue balls, thrice the number of blue balls are the red balls.

•The total number of balls in the bag is 27 .

To find :-

• The number of balls of each colour present in the bag.

Solution :-

Given that

Let the number of white balls in the bag be X

The number of blue balls in the bag

= Twice the number of white balls

= 2×Number of white balls

= 2X

The number of red balls in the bag

= Thrice the number of blue balls

= 3×Number of blue balls

= 3(2X)

= 6X

Total number of balls in the bag

= White balls + Blue balls + Red balls

= X+2X+6X

= 9X

According to the given problem

Total number of balls in the bag = 27

=> 9X = 27

=> X = 27/9

=> X = 3

Therefore, X = 3

The number of white balls = 3

Now,

If X = 3 then number of blue balls

= 2X

= 2(3)

= 6

If X = 3 then the number of red balls

= 6X

= 6(3)

= 18

Answer :-

• The number of white balls = 3

• The number of blue balls = 6

• The number of red balls = 18

Answer 2

Question

$\sf{A \: \: bag \: \: contains \: some \: \: number \: \: of \: \: white \: \: balls, \: \: twice \: \: the \: \: number \: \: of \: white \: \: balls \: \: are \: \: blue \: \: balls \: \: , thrice \: \: the \: \: number \: \: of \: \: blue \: \: balls \: \: are \: \: the \: \: red \: \: balls. \: \: If \: \: the \: \: total \: \: number \: \: of \: \: balls \: \: in \: \: the \: \: bag \: \: are \: \: 27 \: \: Then \: \: calculate \: \: the \: \: number \: \: of \: \: balls \: \: of \: \: each \: colour \: \: present \: \: in \: \: the \: \: bag.}$

Assume

$\sf{Let \: \: the \: \: number \: \: of \: \: white \: \: balls \: \: be \: \: \bold x}$

As per the question,

$\sf{Number \: \: of \: blue \: \: balls = Twice \: \: the \: \: number \: of \: white \: balls}$

So, Number of blue balls= 2×x = 2x

And it is also given that,

$\sf{Number \: of \: red \: balls= Thrice \: the \: number \: of \: blue \: balls }$

So, Number of red balls= 3×2x = 6x

According to the question,

Sum of total number of balls = 27

$\sf \rightarrow \: x + 2x + 6x = 27$

$\sf \rightarrow9x = 27$

$\sf \rightarrow \: x = \frac{27}{9} = 3$

So,

${ \sf \boxed{ \sf{ Number \: of \: white \: balls= 3}}}$

${ \boxed{ \sf{ \blue{Number \: of \: blue \: balls = 2x = 2 \times 3 = 6}}}}$

$\boxed{ \sf{ \red{Number \: of \: red \: balls= 6x = 6 \times 3 = 18}}}$