Out of total number of people in an office, 40% are males. Ratio of number of married to that of unmarried people in the office is 3:2 while ratio of number of married males and married females in the office is 8:7, respectively.  Find the total number of people in the office if the number of unmarried females in the office is 96.

Solution

Let the total number of people in the office be ‘100x’ Number of males in the office = 100x × 0.40 = ‘40x’ Number of females in the office = 100x – 40x = ‘60x’ Total number of married people in the office = 100x × (3/5) = ‘60x’ Total number of unmarried people in the office = 100x × (2/5) = ‘40x’ Number of married males in the office = 60x × (8/15) = ‘32x’ Number of married females in the office = 60x – 32x = ‘28x’ Number of unmarried females in the office = 60x – 28x = ‘32x’ According to question: 32x = 96 x = 3 So, total number of people in the office = 100 × 3 = 300