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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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