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A milkman mixes water and milk in a container in the ratio

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A milkman mixes water and milk in a container in the ratio  [#permalink]

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New post 23 Mar 2019, 06:59
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40% (03:35) correct 60% (03:17) wrong based on 30 sessions

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A milkman mixes water and milk in a container in the ratio of 2 : 5, respectively. Initially, he sells the mixture at $30 per liter. After selling 70 liters of mixture, he mixes another 20 liters of water and then ratio of water and milk becomes 8 : 15, respectively. The new mixture is sold by the milk man at the rate of $25 per liter. If cost of milk is $27 per liter then find the profit of milkman in the whole transaction?

a. $2050
b. $2500
c. $2950
d. $2450
e. $3300

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Intern
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Re: A milkman mixes water and milk in a container in the ratio  [#permalink]

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New post 23 Mar 2019, 18:46
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Original mixture: W/M=2/5
Sold 70L - 20L water, 50L milk

New mixture: add 20L water into mixture
(W-20+20)/(M-50) = 8/15
Original mixture: W=80, M=200
New mixture: W=80, M=150, Total=230

Profit=Revenue-cost
70x30 + 230x25 - 27x200 = 2450

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Re: A milkman mixes water and milk in a container in the ratio  [#permalink]

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New post 09 Apr 2019, 01:10
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The quantity of milk in the 70 liters of the original mixture (M1) that the milkman sold at $30/L is 50 liters. So his cost for was $(50*27)=$1350 and his revenue was $(70*30)=$2100 for the 1st transaction. So his profit for the first transaction (P1) was $(2100 - 1350)=$750.

Let the remaining quantity of M1 be 7x liters of which the quantities of water and milk are obviously 2x and 5x liters respectively. When 20 liters of water is added to this 7x liters of M1, the quantity of milk increases to (2x+20) liters so the ratio of water to milk in this new mixture (M2) becomes (2x+20)/5x which we are told is equal to 8/15. So, (2x+20)/5x=8/15-----> x=30.
Qty of M2=7x+20=230 liters.
Revenue from selling M2=230*25=$5750
Cost of M2=(Qty Of milk in M2)*27=5*30*27=$4050
Profit from 2nd transaction (P2) is $(5750-4050)=$1700

Total profit: P1+P2 $(750+1700)= $2450. Ans:D
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Re: A milkman mixes water and milk in a container in the ratio   [#permalink] 09 Apr 2019, 01:10
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A milkman mixes water and milk in a container in the ratio

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