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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
49% (03:34) correct
51%
(03:24)
wrong
based on 91
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. $2050
B. $2500
C. $2950
D. $2450
E. $3300
Updated on: 30 Dec 2021, 22:54
Originally posted by lovikansal on 12 Dec 2021, 23:33.
Last edited by lovikansal on 30 Dec 2021, 22:54, edited 1 time in total.
Last edited by lovikansal on 30 Dec 2021, 22:54, edited 1 time in total.
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Profit before ratio change:
Milk in mixture: 70 * \(\frac{5}{7}\) = 50 L
Therefore, water in mixture = 70 - 50 = 20 L
Profit = (70*30) - (50*27) = $750
Profit after ratio change:
\(\frac{W}{M}\) = \(\frac{2}{5}\)
W= \(\frac{2M}{5}\)
Since, 70L of mixture (of which 50L was milk and 20L was water) was used and 20L of water was added, the new ratio can be written as:
\(\frac{(W - 20 + 20)}{(M -50)}\) = \(\frac{8}{15}\)
15W = 8M - 400,
using, the highlighted equation, substitute the value of W and then solve the equation to get, M= 200
Enter the value of M in: 15W = 8M - 400, to get W= 80
Total Milk and Water = (W + 20 - 20) + (M - 50) = 80 + 150 = 230L
Profit after ratio change: (230*25) - (150*27) = $1700
Total Profit:
$750 + $1700 = $2450
Hence, option D is the correct answer.
Milk in mixture: 70 * \(\frac{5}{7}\) = 50 L
Therefore, water in mixture = 70 - 50 = 20 L
Profit = (70*30) - (50*27) = $750
Profit after ratio change:
\(\frac{W}{M}\) = \(\frac{2}{5}\)
W= \(\frac{2M}{5}\)
Since, 70L of mixture (of which 50L was milk and 20L was water) was used and 20L of water was added, the new ratio can be written as:
\(\frac{(W - 20 + 20)}{(M -50)}\) = \(\frac{8}{15}\)
15W = 8M - 400,
using, the highlighted equation, substitute the value of W and then solve the equation to get, M= 200
Enter the value of M in: 15W = 8M - 400, to get W= 80
Total Milk and Water = (W + 20 - 20) + (M - 50) = 80 + 150 = 230L
Profit after ratio change: (230*25) - (150*27) = $1700
Total Profit:
$750 + $1700 = $2450
Hence, option D is the correct answer.
13 Dec 2021, 08:23
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Bunuel
S.P for first 70 litres of mixture = 70*30 = 2100.
Amount of milk in that 70 litres = 50 litres. |2x+5x = 70, x = 10 So, 5x = 50.
C.P for 70 litres of mixture = 50*27 = 1350. |27 rate of milk
Profit from first 70 litres = 2100-1350 = 750.
Now coming to the second part:
after adding 20 litres of water new ratio of milk and water is 15:8
Initial ratio = 5:2
so putting in equation
5x:2x+20 = 15:8
Will give x = 30
So amount of milk = 150 litres.
Total quantity = 150 + 60 + 20 = 230 litres.
S.P for 230 litres of mixture = 230 * 25 |rate given in question stem
C.P for 230 litres = C.P for 150 litres of milk = 150*27
Profit = 230*25 - 150*27
On solving we will get 1700.
Now adding profits from both the transaction = 1700+750 = $2450 which is option D
