Aptitude - Ratio and Proportion - Discussion

Is there any shortcuts?

Please correct if I am wrong.

The above problem can be rather simply solved by elimination of the Options:

Milk : 40litres.
Water: 20litres.

What value of water would you add to existing water so that it doubles compared to the quantity of milk (40 litres) present in the mixture : 20 + 60 = 80 (which is now double of 40)

Hence 60 litres.

(m1*w1)/L1 = (m2*w2)/L2.

(2*1)/60 = (1*2)/L2.

2/60 = 2/L2.

2L2 = 120.

L2 = 60.

If 60 liters of the water is added, then the mixture contains only water because the mixture is of 60 liters. What about the milk in the mixture?

Guys can anybody help me with this problem. The length and breadth of a rectangle is 57m and 38m respectively. Find the ratio of the length to breadth.

@Shrikant.

Is this formula applicable of all type of problems?

Here is one shortcut for such type of problems.

Given quantity x lit.

Ratio p : q.
Ratio a : b.

Formula is x(pb-qa)/a(p+q).

Total mixture x=60 ltrs.

a:b=2:1(old ratio) c:d=1:2(new ratio).

x(ad-bc)/c(a+b).

= 60(2*2-1*1)/1(2+1).
= 60(4-1)/3.
= 60*3/3.
= 60 ltrs.

Total mixture is 60ltr which contains milk and water in the ratio 2:1, which means mixture contains 2 parts of milk and 1 part water.

2 parts + 1 part = 3 parts = 60 ltr.

Therefore 1 part =60/3 = 20 ltr.

Milk = 2 parts= 2* 20 =40 LTR.

Water = 1 part=1 * 20 = 20 ltr.

Now quantity of milk and water is changed in such a way to get the new amount of milk and water in the mixture as 1:2.

Now the 1 in 1:2 represent that the amount of milk in the mixture is not changed and it is same as 40ltr. The change is in the amount of water.

Here 1 part in 1:2 represent 40 ltrs of milk. Therefore 2 part 80 ltrs. That is we need 80 ltrs of water to get the new mixture ratio. We have 20 lts of water. Now additional 60 ltrs must be added.

So 60 ltrs is the answer.

Old ratio is 2:1.
New ratio is 1:2.

So new ratio is multiply by 2 we get 2:4 (because we want water only).

Old ratio: 2:1.
New ratio: 2:4.

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0:3
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So (3/sum of old ratio) *60=3/3*60=60 is the answer. This method can be applied to all problems like this.