A container contains 210 L of wine. 70 L is taken out of the container

Question

A container contains 210 L of wine. 70 L is taken out of the container every day and an equal quantity of water is put into it. What is the quantity of the wine that remains in the container at the end of the third day ?

(A) 62 2/9 L
(B) 60 2/9 L
(C) 56 1/2 L
(D) 51 1/9 L
(E) 50 1/9 L

(A) 62 2/9 L 
(B) 60 2/9 L
(C) 56 1/2 L 
(D) 51 1/9 L 
(E) 50 1/9 L

TestPrepUnlimited · Accepted Answer

We take out  \frac{70}{210} = \frac{1}{3}  of the liquid each day, which means we are taking out one-third of wine and water every time before refilling. Therefore  1 - \frac{1}{3} = \frac{2}{3}  of wine is leftover each time we do this.

Repeat three times since we're asking for end of 3rd day.  210 * (\frac{2}{3})^3 = 70*\frac{8}{9} = \frac{560}{9} = 60 + \frac{20}{9} = 62\frac{2}{9} .

Ans: A

Nik11 · Answer

I believe it's a little unclear the fact that he doesn't subtract 70 L each day but actually 1/3 of the wine left.

Said that, we can solve it in this way:

210-70= 140
140 - (140/3)= 280/3
(280/3) - (280/9)= 560/9, simplify and you find 62 + 1/9 ----> A

nityakaul02 · Answer

please provide easier way to deal with this problem

billionaire999 · Answer

Hello Nitya,  nityakaul02

Day 0 = 210 liters of wine

Day 1 end = 210 -70(of mixture is removed) + 70 liters of water added

DAY 1 END 140L wine , 70L Water

Day 2 = 70L out of 210L is removed. 70/210 = 1/3

so 140/3L wine removed, 70/3L water removed, 70L liters water added

DAY 2 END wine left = approx 93 L wine left

DAY 3 again 70 out of 210 liters is removed

i.e. 1/3

93/3 L of wine removed, i.e. 31 liters approx of wine was removed

DAY 3 end

62L of wine approx remaining.

ANSWER A
Hope it helps

Can,Will · Answer

can we do this with C2/C1=(V1/V2)^n ??

bhumikaakhanna · Answer

So,

The volume of the mixture after removing 70L of wine: 140
The volume of the mixture after adding 70L of water: 210
so, 100% (conc. of wine) * 140/210

We do this 3 times so the final concentration of wine= 100%* 2/3 * 2/3 * 2/3

And we know that 
 
Amount of wine= 210* 2/3* 2/3* 2/3 
Amount of wine= 62 2/9

Vibhatu · Answer

Final= Initial(1- amount replaced/total amount)^number of times replaced

by this formula; 
 final amount= 210(1-70/210)^3 
 Answer= 62 2/9 (A)

A container contains 210 L of wine. 70 L is taken out of the container

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A container contains 210 L of wine. 70 L is taken out of the container

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