Problem on Mixture

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seema19: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Sep 14, 2011 12:34 am

by seema19 » Sat Nov 26, 2011 6:06 am

In what ratio should freely available water be mixed with wine worth Rs. 60/- per liter so that after selling the mixture at Rs. 50/- per liter, the profit will be 25%?

A) 1:2
B) 2:3
C) 3:4
D) 4:5
E) 5:6

Answer: A

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Source: Beat The GMAT — Problem Solving | Sat Nov 26, 2011 6:06 am

user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Sat Nov 26, 2011 6:58 am

IMO A

lets say initially there is 1 liter pure wine whose worth is 60 Rs.

given, worth of a liter of mixture = 50 Rs with 25% percent profit
so mixture's actual worth will be 50/1.25 = 40 Rs

amount of mixture with 1 liter pure wine is 60/40 = 1.5 litre
=>in 1.5 liters of mixture we have 1 liter wine & 0.5 liter
so the ratio is 1:0.5 = 2:1

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GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Sat Nov 26, 2011 8:24 am

If we want to make a 25% profit by selling at 50, then we need to sell at x where 1.25x=50 or x=40. The pure wine is worth 60/liter and the water is worth 0/liter. We need to blend them to make it worth 40/liter.

0--------------------40----------60

We start with pure wine that is 60/liter. As we add water that is worth 0/liter, the overall price moves from 60 toward 0. In this case we want the overall price to be 40, which is 1/3 of the way from 60 to 0, so the mixture should be 1/3 water, which means it should be 2/3 wine, which means the water to wine ratio should be 1:2. This should make sense because a 50/50 split would put the overall price right in the middle of 0 and 60, or 30. The price we want is closer to 60, which means the mixture should have more wine.

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sat Nov 26, 2011 8:46 am

I prefer using allegation here,

50@ 25% profit, so mixtures actual worth is 40.

Now 0 and 60 are mixed to form 40.

Using allegations, ratio water and wine should be mixed is (60-40)/(40-0) = 20/40 = 1/2 A

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sat Nov 26, 2011 9:02 am

seema19 wrote:In what ratio should freely available water be mixed with wine worth Rs. 60/- per liter so that after selling the mixture at Rs. 50/- per liter, the profit will be 25%?

A) 1:2
B) 2:3
C) 3:4
D) 4:5
E) 5:6

Answer: A

Rs 50 represents the selling price after the profit ...

So , If Selling price is 125 ( Including 25% profit ) , Cp is 100

If Selling price is 1 , Cp is 100/125

If Selling price is 50 , Cp is ( 100/125 ) *50 = Rs 40

There is a shortcut trick also , if Profit is ( 25% ) 1/4 , Cost price will be 4 / (1+4) times the selling Price...

In fact U can make this as a thumb rule as well , if Profit given is as a / b , and selling price is given S and U wanna find the CP , just use the formula -

CP = b / ( a + b ) * SP

So , Cp = 4 / 5 * 50 => 40

Now we must find a solution very very quickly...

Use shankkar Ashwin's formula and it will come down within 30 seconds..

Abhishek

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Nov 26, 2011 3:55 pm

seema19 wrote:In what ratio should freely available water be mixed with wine worth Rs. 60/- per liter so that after selling the mixture at Rs. 50/- per liter, the profit will be 25%?

A) 1:2
B) 2:3
C) 3:4
D) 4:5
E) 5:6

Answer: A

Another efficient approach would be to plug in the answers.

Answer choice C: 3 liters of water for 4 liters of wine.
Cost of 4 liters of wine = 4*60 = 240.
Selling price of the 7 liter mixture = 7*50 = 350.
Profit = 350-240 = 110.
Since (.25)240 = 60, the profit is almost DOUBLE what is required.
To decrease the profit by almost 50%, the proportion of wine in the mixture must increase SUBSTANTIALLY.
The correct answer is almost surely A.

Answer choice A: 1 liter of water for 2 liters of wine.
Cost of 2 liters of wine = 2*60 = 120.
Selling price of the 3 liter mixture = 3*50 = 150.
Profit = 150-120 = 30, a profit of 25%:
.25(120) = 30.

The correct answer is A.

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