Mixtures and Alligations - Vikas Saini
A 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 litre solution of 45% alcohol. How much of 30% solution was used.
(a) 2 ltr
(b) 2.5 ltr
(c) 2.7 ltr
(d) 3.2 ltr
(e) 3.7 ltr
(50-45 ) : (45-30)
5 : 15 = 1 : 3.
Ratio = 1 : 3
30% solution was added = 10 x 1 / (1 + 3) = 2.5 ltr.
The percentage volumes of milk in three solutions A,B and C form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 2:3:4, by volume we obtain solution containing 32% milk. If we mix them in the ratio 3:2:1, by volume, we obtain a solution containing 22% milk. What is the percentage of milk in A?
Suppose volumes of milk percentage in A,B,C are a, ar, ar^2 respectively.
2a + 3ar + 4ar^2 = 32 x 9.
3a + 2ar + ar^2 = 22 X 6.
a= 12, r = 2.
The percentage of milk in A = 12%.
One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight ?
X-16 : 16 - 10
1 : 1/3
X – 16 / 6 = 3 / 1
X = 34.
From a solution that has milk and water in the ratio 5 : 3, ‘x’ percent is removed and replaced with water. The concentration of milk in the resulting solution lies between 30% and 50%. Which of the following best describes the value of ‘x’?
a) 25 < x < 30
b) 20 < x < 52
c) 20 < x < 48
d) 25 < x < 60
Suppose total unit is 8. Milk = 5, water = 3.
X% of 8 is removed = 0.08x.
Where milk part is 0.05x and water part is 0.03x.
0.30 < 5 – 0.05x / 8 < 0.50
2.40 < 5 – 0.05 x < 4.0
-2.60 < -0.05x < -1.
1 < 0.05x < 2.6
20 < x < 52.
The concentration of milk in 60L milk and water solution is 30%. If 6L of the solution is replaced by water then 5L solution is again replaced by water, then find the concentration of milk in the final solution.
a) 24.50 %
c) 24.75 %
The concentration in final solution = (3/10) ( 1 - 6/60) (1 – 5/60)
Rice of two different qualities are mixed and the mixture is sold at rs. X per kg, giving 25% profit. If higher quality rice is sold at rs X per kg, then there will be a loss of 100/11 %. If the ratio of the quantities of the lower quality rice and the higher quality rice in the mixture is 8 : 3, then what is the percentage profit when lower quality rice is sold at X per/kg ?
Cost price of low quality rice per kg is l and cost price of high quality rice per kg is h.
(8l + 3h / 11)(5/4) = h (10/11)
8l = 5h.
Cost price of lower quality rice is 5h/8.
Selling price of mixture = 10h/11.
Profit percentage = (10h/11 – 5h/8) x 100 / (5h/8) = 500/11 %.
Two containers X and Y, equal quantities of water and acid. The concentration of acid is same in both the containers X and Y. If 4 litres of solution from X is replaced by acid and the concentration of acid becomes twice what it was initially. If 8 litres of solution is from Y is replaced with pure acid then what is the ratio of final concentration of acid in solution Y to the initial concentration of acid in solution Y ?
Suppose quantity is q, concentration of acid = a, suppose quantity of water.
In container X, 4 litre acid is replaced then concentration becomes twice.
In container Y, 8 litre acid is when replaced then concentration becomes two times of twice.
Hence increases by thrice.
Ratio = 3 : 1.
A and B are two perfumes which have oil and essence in the ratio of 11:3 and 2:5 respectively.
New perfume is made by mixing A and B in the ratio of a:b such that the percentage of oil in the new perfume is 50%. Find a+b.
Oil in A = 11 / 3+11 = 11/14.
Oil in B = 2 / 2+5 = 2/7.
(11a/14) + (2b/7) = (a+b)/2
11a + 4b = 7a + 7b
a/b = ¾
a+b = 7.