Question

One vegetable warehouse had 210 tons of potatoes, another one had 180 tons. 90 tons of potatoes were delivered to the first warehouse every day and 120 tons to the second warehouse. In how many days will the first warehouse have 1.2 times less potatoes than the second warehouse? I think it's 6 days.

Answer 1

Required number of days = 6

Explanation:

Let n be the required number of days

First warehouse

Number of potatoes which are initially in the warehouse = 210 tons

Number of potatoes delivered daily to the warehouse = 90 tons

⇒ Total quantity of potatoes in first warehouse = 210 + 90n

Second warehouse

Number of potatoes which are initially in the warehouse = 180 tons

Number of potatoes delivered daily to the warehouse = 120 tons

⇒ Total quantity of potatoes in second warehouse = 180 + 120n

Now, we need to find number of days when the first warehouse have 1.2 times less potatoes than the second warehouse.

⇒ 180 + 120n = 1.2 (210 + 90n)

⇒ 180 + 120n = 252 + 108n

⇒ 120n - 108n = 252 - 180

⇒ 12n = 72

⇒ n = 6

Hence, Required number of days = 6