Question

In a party 55 persons were present .40% of women wore earings and the remaining 60% wore googles .among the men 50% wore goggles .total number of goggles in the party were 1.5 times the number of earrings .find total number of eaarings

Answer 1

Given :

Total number of persons in the party = 55

percentage of women wore earings = 40%

percentage of women wore googles = 60%

percentage of men wore googles = 50%

Total number of goggles in the party were 1.5 times the number of earrings .

To Find :

Total number of earings

Solution :

Let The number of women = x

The number of men = 55 - x

According to question,

Number of women wore earings = 40% of (x)

And

Number of women wore googles = 60% of ( x)

Again

Number of men wore googles = 50% of  (55 - x)

Since,

Total number of goggles in the party =  1.5 times the number of earrings  

i.e 60% of (x) + 50% of (55- x ) = 1 .5 × 40% of ( x) × 2

Or, 50 × (55 - x)  = 1 .5 × 40 × (x) × 2- 60 x

Or,  2750 - 50 x = 120 x - 60 x

or,  2750 = 60 x + 50 x

Or, 110 x = 2750

∴         x = $\dfrac{2750}{110}$

i.e       x = 25

So, The number of women = x = 25

And,

Number of women wore earings = 1.5 × 40% of (x) × 2 = 1.5 × 40% × 25 × 2

                                                                                           = 30

Hence, The total number of earing is 30 . Answer