Question
Quantity I: The average age of
Aman, Bishnu, and Chinu is 22 years, and the average age of Bishnu, Chinu, and Dharmu is 20 years. If Aman's age lies between 28 and 32 years (inclusive), what is the age of Dharmu? Quantity II: Pawan and Qureshi together can finish a task in 6.75 hours, while Pawan and Rishu together can finish the same task in 6 hours. If the ratio of Qureshi's efficiency to Rishu's efficiency is 2:3, how much time would it take for Qureshi to complete the task alone? In the question, two quantities I and II are given. You have to solve both the quantities to establish the correct relation between Quantity-I and Quantity-II and choose the correct option.Solution
ATQ, Quantity I: Since, Aman + Bishnu + Chinu = 3 × 22 = 66 ----------(1) And, Bishnu + Chinu + Dharmu = 3 * 20 = 60 ---------- (2) By equation (1) – equation (2): Aman – Dharmu = 6 Since, Aman’s is age neither more than 32 years nor less than 28 years. If Aman’s age is 32 years. So, Dharmu’s age = 32 – 6 = 26 years If Aman’s age is 28 years. So, Dharmu’s age = 28 – 6 = 22 years So, the possible ages of Dharmu are 22 years, 23 years, 24 years, 25 years and 26 years. Quantity II: Since, ratio of Qureshi’s efficiency to Rishu’s efficiency is 2: 3. Let the time, in which Qureshi alone can Rishu alone can complete the work are ‘3t’ hours and ‘2t’ hours respectively. So, (1/Aman) + (1/3t) = 1/6.75---------(1) And, (1/Aman) + 1/2t= 1/6--------(2) From equations (1) and (2): 1/6.75- 1/3t= 1/6- 1/2t 1/2t- 1/3t= 1/6- 1/6.75 (3-2)/6t = (9-8)/54 t = 9 So, the time, in which Qureshi alone can complete the task = 3 × 9 = 27 hours
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