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SSC Selection Post 2020 PYQ — Question 52

SSC Selection Post - Matriculation Level - 9 Nov 2020 - Shift 3 • Quantitative Aptitude • Q52

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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?
 

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 156.

 

The average height of males =  x + 5 %  of  x = x + 0.05x = 1.05x 

From the ratio 7:6, total parts = 7 + 6 = 13

Males =  713×78=42\frac{7}{13} \times 78 = 42

Females = 613×78=36\frac{6}{13} \times 78 = 36

Total height of all = Total average × Total people = 160.2 × 78 = 12,495.6 cm

Height from males  +  Height from females = 42 × 1.05x + 36 × x

= 42 × 1.05x + 36x =44.1x + 36x = 80.1x

80.1x = 12,495.6 ⇒ x = 12,495.6 ⇒x=12,495.680.1=156\Rightarrow x = \frac{12,495.6}{80.1} = 156