Question

In a group of 78 persons, the ratio of the numbers of males and females is 7 : 6. The average height of all the persons is 160.2 cm. If the average height of males is 5% more than that of females, then what is the average height (in cm) of females in the group?
1. 157.6
2. 158
3. 156.4
4. 156

Answer 1

Correct Answer - Option 4 : 156

Given:

The total number of person is 78.

Calculation:

Let be assume the average height of female is p

⇒ Total male = 78 × (7/13) = 42, Total female = 78 - 42 = 36

⇒ Total height of all person = 160.2 × 78 = 12495.6

⇒ The average height of males = p × (105/100) = 21p/20

⇒ Total sum of height of male = (21p/20) × 42 = 44.1

⇒ Total sum of height of female = p × 36

⇒ 36p + 44.1p = 12495.6

⇒ 80.1p = 12495.6

⇒ p = 156

∴ The required result will be 156.