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Sixty percent of the teachers of a certain school are male and three - fifth of the male teachers earns more than Rs. 35,000 per year. If 45% of the schools teachers earn more than Rs. 35,000 per year, what percentage of the female teachers of the school earn Rs. 35,000 or less per year?

Sixty percent of the teachers of a certain school are male and three - fifth of the male teachers earns more than Rs. 35,000 per year. If 45% of the schools teachers earn more than Rs. 35,000 per year, what percentage of the female teachers of the school earn Rs. 35,000 or less per year? Correct Answer 77.5%

GIVEN :

Sixty percent of the teachers of a certain school are male and three - fifth of the male teachers earns more than Rs. 35,000 per year.

If 45% of the schools teachers earn more than Rs. 35,000 per year.

 

ASSUMPTION :

Let the total number of teachers in the school be x

 

CALCULATION :

Then the number of male teachers and female teachers be 0.60x and 0.40x respectively.

The number of male teachers earn more than Rs. 35000

                                                                       = 3/5 × 0.6 x

                                                                       = 0.36 x

Total number of teachers earning more than Rs. 35000

                                                                       = 45% of x

                                                                       = 0.45 x

Number of female teachers earning more than Rs. 35000 =

Total teachers earning more than Rs. 35000 – total number of male earning more than Rs. 35000

= 0.45 x – 0.36 x 
⇒ 0.09 x

Number of the female teachers earning Rs. 35000 or less

                                                                   = 0.40x – 0.09x

                                                                   = 0.31x

∴ Percentage of the female teachers who earn Rs. 35000 or less

                                                                  = (0.31x/0.40x) × 100

                                                                  = 77.5%

 

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