A tank has a solution consisting of milk and water in equal proportio

Question

A tank has a solution consisting of milk and water in equal proportion. This solution is transferred into a vessel having 100 ml pure water at the rate of 10 ml per second. In how much time from the start of the transfer, will the ratio of milk to water in the vessel be 1 : 3?

(A) 5 seconds
(B) 10 seconds
(C) 15 seconds
(D) 20 seconds
(E) 25 seconds

(A) 5 seconds
(B) 10 seconds
(C) 15 seconds
(D) 20 seconds
(E) 25 seconds

PB005 · Accepted Answer

Lets say we have 200ml water+milk mixture (each one is 100 ml). Given rate of flow : 10ml per sec so say 5ml per sec for water and 5 ml per sec for Milk, and the tank already contains 100ml water.
so at t=0, Milk in tank=0ml and water in tank = 100ml.
at t=1sec, milk = 5ml and water = 100 + 5ml
so we get AP for milk=5n and water 100+5n at time n sec.
using the ratio given, M:w=1:3 we solve it using 5n/(100+5n)=1/3 so get n=10 sec.

Nidzo · Answer

1 : 3 milk to water can be expressed as 25% milk

Using alligation: the solution that will be poured in has 50% milk, where the 100ml in the vessel has 0%

50..........0
.......25......
25...........25

or 1:1

As equal parts of both are required to form a 25% solution, and the vessel has 100ml, then 100ml of the 50/50 solution is needed.

100ml being poured at 10ml/second will take 10 seconds to pour. 
Answer B

stne · Answer

Let initially there be  100  ml. of soln.

So  50\%  , i.e. 50  ml. is milk before transfer.

let  x  ml of soln. be transferred to achieve the required ratio.

After transfer quantity of milk is  \frac{1}{4}* ( 100 + x )

Note: Amount of Milk remains constant before and after transfer.

So  50 = \frac{1}{4}* ( 100 + x )

x= 100

So  100  ml. of soln. was transferred.

Since rate of soln. transfer is  10  ml per second , it will take  \frac{ 100 }{10} =10   s. for the required quantity to transfer.

Ans-B

Hope it's clear.

glennc · Answer

Total solution = 80 L
 Milk : Water = 4 : 3
Initial milk = (4/7) × 80 = 320/7 L
Each operation removes 10 L out of 80 L, so fraction of milk retained each time = 70/80 = 7/8
Operation is done 3 times:
Milk left
 = (320/7) × (7/8)3
 = (320/7) × (343/512)
 = (5 × 49)/8
 = 245/8 L
 Answer: 245/8 litres (Option A)

A tank has a solution consisting of milk and water in equal proportio

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A tank has a solution consisting of milk and water in equal proportio

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards