Given below are three quantities named A, B and C. Based on the given information, you have to determine the relationships between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. The options represent the relations among the three quantities. A. C. ≤ D. ≥ E. = Quantity A: The average of a batsman after 75 innings was 83 runs per innings. If after the 76th inning his average drops by 1 run, then what was his score in the 76th inning? Quantity B: The average marks of a group of 20 students on a test are reduced by 4 when the topper who scored 87 marks is replaced by a new student. How many marks did the new student have? Quantity C: The average age of a husband and wife was 23 years when they were married 5 years ago. The average age of the husband, the wife, and a child who was born during the interval, is 20 years now. How old is the child now? Correct Answer E B Quantity A: Sum of the runs scored in 75 innings = 83 × 75 = 6225 Sum of the runs scored in 76 innings = (83 – 1) × 76 = 6232 Runs scored in the 76th inning = 6232 – 6225 = 7 ∴ Runs scored in the 76th inning = 7 Now, Quantity B: Let the initial average be ‘x’. Sum of the marks of all the students initially = 20 × x = 20x Sum of the marks of all the students when the topper is replaced by a new student = 20(x – 4) = 20x – 80 ⇒ The new student has 80 marks less than the topper. ⇒ Marks secured by the new student = 87 – 80 = 7 ∴ Marks secured by the new student = 7 Quantity C: Let present ages of husband, wife and child be m, n and p years respectively. Given, ⇒ / 2 = 23 ⇒ m + n = 46 + 10 = 56 Given, ⇒ (m + n + p)/3 = 20 ⇒ m + n + p = 60 ⇒ 56 + p = 60 ⇒ p = 4 ∴ Child is 4 years old now. ∴ Quantity A = Quantity B > Quantity C