Question

In a group of persons, average weight is 60 kg. If the average weight of males and females taken separately is 80kg and 50kgq respectively, find the ratio of the number of males to that of females.
A) 2:3 B) 3:2
C) 2:1 D) 1:2

Answer 1

Take the no. Of male as x and females as y.total no. Of people = x+y

Therefore total weight = avg weight x( y+x).

Total weight = 60(x+y)

Now total weight of male = 80x and total weight of females=50y,therefore total weight = 80x +60y

But,total weight=60(x+y)=80x+50y

60x+60y=80x+50y

10y=20x

=] Y=2x

X:y= 1:2

Answer 2

The ratio of the number of males to that of females = 1 : 2

Given :

• In a group of persons, average weight is 60 kg.

• The average weight of males and females taken separately is 80kg and 50kg respectively

To find :

The ratio of the number of males to that of females is

A) 2 : 3

B) 3 : 2

C) 2 : 1

D) 1 : 2

Solution :

Step 1 of 2 :

Form the equation to calculate the ratio

Let number of males = m and number of females = n

∴ Total number of persons in the group = (m + n)

Since average weight is 60 kg

∴ Total weight = 60(m + n) kg

Again average weight of males and females taken separately is 80kg and 50kg respectively

∴ Total weight = (80m + 50n) kg

By the given condition

$\displaystyle \sf 80m + 50n = 60(m + n)$

Step 2 of 2 :

Calculate the ratio

$\displaystyle \sf 80m + 50n = 60(m + n)$

$\displaystyle \sf{ \implies }80m + 50n = 60m + 60n$

$\displaystyle \sf{ \implies }80m - 60m = 60n - 50n$

$\displaystyle \sf{ \implies }20m = 10n$

$\displaystyle \sf{ \implies } \frac{m}{n} = \frac{10}{20}$

$\displaystyle \sf{ \implies } \frac{m}{n} = \frac{1}{2}$

$\displaystyle \sf{ \implies }m :n = 1 : 2$

∴ Ratio of the number of males to that of females = 1 : 2

Hence the correct option is D) 1 : 2

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