Mathematics Problem Solving 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 .

A. 12 days B. 20 days C. 18 days D. 15 days SSC CGL 2019 Tier 1 4 March 2020 Shift 1 Solution: In this question from Time and Work , Let us see the shortcut method first: Let us assume the efficiency of A be 4 (it means A can do 4 units of work in a day) Therefore, the efficiency of B will be = 125% of the efficiency of A = 5 (it means B can do 5 units of work in a day) Therefore, the efficiency of C will be = 120% of the efficiency of B = 6 (it means B can do 6 units of work in a day) Total units of work = 30 x 4 = 120 units Total work done by A, B and C in 3 days = (4 + 5 + 6) x 3 = 45 units Remaining work = 120 - 45 = 75 units The number of days required by B to complete the remaining work = 75/5 = 15 days. Hence, (D) is the correct answer. Let us see the basic method: The efficiency of A = One day work of A = 1/30 The Efficiency of B = One day work of B = 1/30 + (25/100) x (1/30) = 1/30 + 1/120 = 1/24 The Efficiency of C = One day work of C = 1/24 + (20/100) x (1/24) = 1/24 + 1/120...