Quant Boosters  Vikas Saini  Set 1

Short approach :
Cp of ball = selling price of all balls / (total balls – loss(no of balls)
= 720 / (175 )
= 60 rs.

Q17) A, B and C start simultaneously from X to Y. A reaches Y, turns back and meet B at a distance of 11 km from Y. B reached Y, turns back and meet C at a distance of 9 km from Y. If the ratio of the speeds of A and C is 3:2, what is the distance between X and Y?

Suppose distance between X and Y is D km.
A = D+11, B = D11.
B = D+9, C = D9.
A/C = 3:2.
(AB) / (BC) = 3/2.
(D+11) (D+9) / (D11) (D9) = 3 / 2.
D^2 + 20D + 99 / D^2 – 20D + 99 = 3 / 2
2(D^2 + 20D + 99) = 3(D^2 – 20 D + 99)
D^2 – 100 D + 99 = 0.
D = 99.

Q18) A shopkeeper uses a weight of of 460 gm instead of 500 gm and sells the article at the cost price. What is profit percentage ?
a. 40%
b. 23%
c. 8 +16/23 %
d. 20%

Short approach :
Profit percentage = [ (500 – 460)/460] x 100
= (40/460) x 100

Q19) 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

By allegation
30  50
 45 
(5045 ) : (4530)
5 : 15 = 1 : 3.
Ratio = 1 : 3
30% solution was added = 10 x 1 / (1 + 3) = 2.5 ltr.

Q20) 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?
a) 6%
b) 12%
c) 18%
d) 24%

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%.

Q21) 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 ?

10  X
 16 
X16 : 16  10
1 : 1/3
X – 16 / 6 = 3 / 1
X = 34.

Q22) 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.
Option B

Q23) 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 %
b) 25.00%
c) 24.75 %
d) 25.50%

The concentration in final solution = (3/10) ( 1  6/60) (1 – 5/60)
= 24.75%.

Q24) 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 %.

Q25) 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.

Q26) 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.