An overhead water tank in a locality has certain amount of water in it. Additionally it receives some amount of water from municipal corporation on a daily basis. Each resident in the locality consumes a fixed amount of water every day. If there were 120 residents, the water would last for 50 days. Instead if there were 125 residents, the water would last for only 40 days. How long will the water last if there were 110 residents.
Explanation:
Let the amount of water initially in the tank = V liters, amount supplied by municipal corporation every day = d liters/day consumption rate of each resident = c liters/day
If there were 120 residents, the water would last for 50 days ⇒ V + 50 × d = c × 120 × 50 …(1)
If there were 125 residents, the water would last for only 40 days ⇒ V + 40 × d = c × 125 × 40 …(2)
Solving (1) and (2), we get ⇒ 6000c – 50d = 5000c – 40d ⇒ 1000c = 10d ⇒ d = 100c
From (1) ⇒ V + 5000c = 6000c ⇒ V = 1000c
Let the water last for x days when there are 110 residents ⇒ V + x × d = c × 110 × x ⇒ 1000c + 100cx = 110cx ⇒ 1000c = 10cx ⇒ x = 100 days.
Hence, option (b).
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