The ratio of Boys and Girls in a group is 7 : 6. If 4 more boys join the group and 3 girls leave the group, then the ratio of boys to girls becomes 4 : 3. What is the total number of boys and girls initially in the group?
A. 78 B. 104 C. 117 D. 91 SSC CGL 2019 Tier - 1 4 March 2020 Shift 2 Solution: Let the number of boys and number of girls initially be x and y respectively. It is given that, x/y = 7/6 6x - 7y = 0 ............(1) If 4 more boys join the group and 3 girls leave the group Number of boys in the group = x + 4 Number of girls in the group = y - 3 New ratio is (x + 4)/(y - 3) = 4/3 3x + 12 = 4y - 12 3x - 4y = -24 ............(2) Multiply equation 2 by 2 and subtract from equation 1, we get y = 48 Put y = 48 in eq 1, we get, 6x - 7 * 48 = 0 x = 56 The number of boys and girls initially in the group = x + y = 48 + 56 = 104 Hence, (B) is the correct answer. This question is based on the topic of Ratio and Proportion .