### Question 4

SSC-CGL 2019 June 13 Shift 1

In a class of 50 students, 40% are girls. The average marks of the whole class are 64.4 and the average of the boys' marks is 62. What is the average marks of the girls?

- 67
- 66.8
- 66.4
- 68

### Solution in Short

Required average = A. Weighted average is 62 x 0.6 + A x 0.4 = 64.4, which can be simplified to obtain A = 68 answer!

### Solution in Detail

Girls in the class are $\displaystyle 40\% \text{ of } 50 = 20$

$\displaystyle \therefore $ boys are $\displaystyle 50 - 20 = 30$

[1] Average score of boys given as $\displaystyle 62$

$\displaystyle \therefore $ total score of boys $\displaystyle 62 \times 30 = 1860$

[2] Average of whole class given as $\displaystyle 64.4$

$\displaystyle \therefore $ total of whole class $\displaystyle 64.4 \times 50 = 3220$

$\displaystyle \therefore$ total of girls = $\displaystyle 3220 - 1860 = 1360$

$\displaystyle \therefore $ average of girls $\displaystyle = \frac{1360}{20} = 68$ ans!

### Solution by Mixtures

Class is a mixture (boys + girls)

[1] Average of boys is 62, and of girls is x

[2] Ratio of boys to girls is $\displaystyle \frac{60\%}{40\%} = \frac {60}{40}$

[3] Average of mixture = 64.4 (given)

Draw the diagram as below

On calculation, x = 68 answer!

This Blog Post/Article "(solved)Question 4 SSC-CGL 2019 June 13 Shift 1" by Parveen is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.