Question

Kevleen invited $ 24 $ of her friends to her birthday party. In the party the ratio of boys and girls was $ 3:5 $ (excluding Kavleen). Find the number of boys and girls invited by Kavleen to her birthday party.

Answer 1

Hint: For ratio given questions always convert ratio to normal by introducing unknown variables and then using the given condition in question to form an equation. In solving so formed equations we can find unknown variables that we introduce earlier. After getting an unknown variable we use it to get required values which are asked in the given question.

Complete step-by-step answer:
Total number of friends invited by Kavleen on her birthday party are $ 24 $ .
Ratio of boys to girls in the party not including Kavleen is $ 3:5 $ .
Writing given ratio of boys to girls in normal form by introducing an unknown variable say ‘x’.
Therefore number of boys in party = $ 3x $
Number of girls in party (not including Kavleen) = $ 5x $
But, as total friends invited by Kavleen on her birthday party was given and equal to $ 24. $

Hence, sum of boys and girls (not including Kavleen) must be equal to $ 24. $
 $
  3x + 5x = 24 \\
   \Rightarrow 8x = 24 \\
   \Rightarrow x = \dfrac{{24}}{8} \\
   \Rightarrow x = 3 \\
  $
Using, above calculated value of ‘x’ to find the number of boys and girls in the party.
Number of boys in Kavleen party = $ 3x $
Or $ 3\left( 3 \right) = 9 $ $ \left( {\because x = 3} \right) $

Number of girls in Kavleen party (not including Kavleen) = $ 5x $
Or $ 5\left( 3 \right) = 15 $ $ \left( {\because x = 3} \right) $
Hence, from above we see that the number of boys and girls invited by Kavleen in her birthday party was $ 9 $ and $ 15 $ respectively.

Note: In case of ratio giving problem first express ratio as normal by introducing unknown variable and then using condition given in question to find unknown variable and so on to simplify the required solution of the problem. Remember that equality of two ratios is called proportion which is used in comparison of two ratios.