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# Quant Quiz On Mixtures & Alligations Day 23 Bag

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## Quant Quiz On Mixtures & Alligations Day 23 Bag

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• The ratio of A & B in a mixture is 8:1, 15ltr of mixture is taken out and same amount of B is added, now ratio become 4:3. Find the initial amount of A in the mixture (approx)?
A) 24
B) 37
C) 34
D) 40
E) 28
Option B
Solution:
initial …………A : B
.                      8 : 1 →(1)
Find                4 : 3 →(2)
Make value of A same, multiply by 2 in equation (2)
A : B
8 : 1
8 : 6 (+5)
5 = 15
1=3
8+6=14 =42
So initial = 8/9 *42 = 37.33
• A shopkeeper sells his milk at cost price but he add some water and earn 16(2/3)% profit. Find the ratio of milk and water?
A) 6:1
B) 1:6
C) 5:1
D) 1:5
E) 5:6
Option A
Solution:
In this case we will let milk 100 and water profit
Milk : Water
100 : 16(2/3)%
6 : 1
• There is 70ltr milk in a container. From this 7ltr of milk is taken out and added some quantity of water. This process is repeated two more times. Find the remaining milk in container?
A) 45ltr
B) 48.03ltr
C) 50ltr
D) 51.03ltr
E) 56.22ltr
Option D
Solution:
7/70 =1/10,  Remaining =9/10
(9/10)T * Total = Milk
(9/10)³ * 70 = 51.03 ltr
• A man has to distribute Rs65 in a class of 50 students. He gives 1.5 rupee to boys and 1 rupee to girls each. Find how many girls are there in the class?
A) 30
B) 20
C) 15
D) 25
E) 22
Option B
Solution:
Mean price = 6500/50 = 130 paisa
Boys………..Girls
150………….100
.         130
30…………….20
3 : 2
2/ 5* 50 = 20
• In an alloy the ratio of copper and aluminum is 4:5 and in other alloy the ratio of copper and aluminum is 6:7. In what ratio these alloy should be taken to make ratio of copper and aluminum is 5:6?
A) 5 : 11
B) 11 : 5
C) 13 : 9
D) 9 : 13
E) 12 : 7
Option D
Solution:
C………………..A
4/9……………6/13
.         5/11
1/143………….1/99
9 : 13
• In a bag there are three types of coins, 1rupee, 50 paisa and 25paisa in the ratio of 5:10:24. There total value is Rs208. The total number of coins is?
A) 507
B) 208
C) 961
D) 744
E) 602
Option A
Solution:
first make ratio according to rupee
5 : 10/2 : 24/4
5 : 5 : 6
16 =208
1 =13
(5+10+24) = 39 = 39*13 = 507
• 400gm of sugar solution has 30% sugar in it. How much sugar should be added to make it 50% in the solution (in gm)?
A) 120
B) 60
C) 100
D) 160
E) 180
Option D
Solution:
30% of 400 =120
Remaining =280, this will remain same in another solution but now it will become 50%. So
50% = 280
100% = 560
Difference = 560-400 = 160
• A mixture of certain quantity of milk with 15ltr of water is sold at 80paisa/ltr. If pure milk be worth Rs1.10 per ltr. How much milk is there in the mixture?
A) 50 ltr
B) 40 ltr
C) 60 ltr
D) 70 ltr
E) 30 ltr
Option B
Solution:
Milk……..Water
110………….0
.        80
80………….30
8 : 3
3 = 15, so 8 = 40
• A merchant borrowed Rs3500 from two money lenders. For one loan he paid 14% p.a and for other 18% p.a. the interest paid for one year was Rs525. How much did he borrow at 18%p.a?
A) Rs875
B) Rs625
C) Rs750
D) Rs1000
E) Rs925
Option A
Solution:
525/3500 * 100 = 15%
14………….18
.        15
3……………..1
1/4 * 3500 = 875
• How many kg of salt at42 paisa per kg must a man mix with 25kg of salt at 24 paisa per kg, so that he may on selling the mixture at 40 paisa per kg, gain 25% on the outlay?
A) 15kg
B) 20kg
C) 25kg
D) 30kg
E) 18kg
Option B
Solution:
25% =1/4
CP……….SP
4………….. 5
4 = 32, 5 = 40
42…………24
.        32
8…………..10
4 : 5→*5= 25kg
So 4 * 5 = 20
1. A shopkeeper sells two types of books national books and international books .He sells national books at Rs. 18 / book  and incurs at loss of 10% whereas on selling the international books at Rs. 30 / book ,he gains 20 % .Find the ratio of the national and international books such that he can gain a profit of  25% by selling the combined books at 27.5/ book ?
A)  5:6
B)  5:2
C)  4:5
D)  2:3
E)  4:7
Option  B
Solution:
Loss at national books =  10% = 1/10
SP -> 9 = 18
1 = 2
CP -> 10 = 20
Gain at  international books = 20 % = 1/5
SP -> 6 = 30
1 = 5
CP ->5 = 25
CP = 4 *5.5  = 22
National Books                            International Books
20                                                          25.                                 22
5                                                              2

2. One test  tube contains some acid and another test tube contains an equal quantity of water .To prepare a solution , 20 g of the acid is poured into the second test tube .Then , two –third of the so- formed solution is poured from the second tube into the first .If the fluid in the first test tube is four times that in the second ,what quantity of water was taken initially ?
A)  90 g
B)  70 g
C)   154 g
D)  100g
E)   180 g
Option  D
Solution:
Let x g of water was taken initially .
1st process
First test tube (x- 20)
second test tube (x +20)
2nd process
First test tube = [(x-20) +2/3 (x+20)] Second test tube = 1/3(x+20)
Now ,
(x -20 ) + 2/3(x+20) = 4* (1/3)(x+20)
=> x = 100 g

3. Two brands of detergents are to be combined . Detergent  A contains  40 % bleach and 60 % soap . While detergent  B contains  25 % bleach and  75%  soap . If the combined mixture is to be 35 % bleach .What % of the final mixture should be detergent A?
A)  30%
B) 45.64%
C)   20%
D)  32.5%
E)  66.67%
Option E
Solution:
A                                                         B
40                                                       25
.                               35
10                                                           52   :    1
Therefore ,
% of detergent in A = (2 /3) *100 =
4. A thief has stolen  15 L of beer from a container and replaced with the same quantity of water .He again repeated this process 3 times .Thus the ratio of the beer become 343 :169 .Find the initial amount of beer in the container .
A)  90 L
B) 120 L
C) 140 L
D)  110 L
E)  80 L
Option B
Solution: The initial amount of beer in the container was =343 + 169 = 512 L
Initial amt. of beer  : After mixed with water
512 : 343
Taking cube roots on both the sides,
8 :7
For 1 unit of beer -> 15 L
For 8 units of beer -> 120 L
5. A tank which contains a mixture of syrup and water in ratio 15:6. 25.5 litres of mixture is taken out from the tank and 2.5 litres of pure water and 5 litres of syrup is added to the mixture. If resultant mixture contains 25% water, what was the initial quantity of mixture in the tank before the replacement in litres?
A)  77.7
B)  70.78
C) 75.6
D)  80.5
E)  76
Option  A
Solution:
Quantity of Syrup = 15x
Quantity of water =6x
Total = 21x
Resultant Mixture = 21x – 25.5 + 2.5 + 5 = 21x – 18
Resultant water = 6x – 25.5 * (6/21) + 2.5 = 6x – 7.28
Resultant mixture contains 25% water
(21x – 18)*25/100 = 6x – 7.28
x = 3.7
Initial quantity = 21*3.7 = 77.7
6. Ram covered a distance of 200km  in 10 hrs . The first part of his journey is covered by auto ,then he hired a car  .The speed of the auto and car is  15 km/hr and  30 km /hr resp. Find the ratio of distance covered by auto and car .
A)  3 : 4
B)  2 : 1
C)  1 : 1
D)  2: 3
E)  None of these
Option C
Solution:
Speed of the Ram = 200 /10 = 20 km/hrAuto                       Car
15km/hr              30km/hr.                    2010                   :                5
2                    :                1Now ,
Ratio of  distance covered :
Auto                  :            Car
2 * 15                 :             1 *30
30                   :            30
1           :                               1

7. 9 L  are drawn from a cask full of water and it is  then filled with milk , 9 L of mixture are drawn and the cask is again filled with milk .The quantity of water now left in the cask to that of the milk in it is 16 : 9 .How much does the cask hold ?
A)  30 L
B)  45 L
C)  35 L
D)  50 L
E)  42 L
Option B
Solution:
16 – > water
25 – > milk
=> √(16/25) = 4/5
If 1 -> 9
then 5 = 45 litres
8. If  2 kg metal , of which (1/3) is zinc and the rest is copper , be mixed with 3 kg of metal , of which (1/4) is zinc and the rest is copper . What is the ratio of zinc to copper in the mixture ?
A)  11 : 43
B)  15 : 37
C) 17 : 43
D) 23 : 74
E)  18 : 52
Option C
Solution:
Quantity of zinc in the mixture = 2 (1/3) + 3 (1/4) = ( 2/3) + (3/4)
=17/12
Quantity of copper in the metal =  (3+2) – (17/12) =  43/12
Therefore , 17 / 12 : 43 /12 = 17 : 43
9. Vessels  A and B contain mixtures of milk and water  in the ratios 4 : 5 and 5 : 1 resp .In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5 : 4 ?
A)  5 : 2
B)  7 : 5
C)  6 : 11
D)  8 : 5
E)  9 : 4
Option A
Solution:
Quantity of milk in vessel A = 4 / (4+5) = 4/9
Quantity of milk in vessel B = 5/(5+1) = 5/6
Quantity of milk in resultant mixture = 5 /( 5+4) = 5/9
A                                 B
4/9                              5/6
.                5/9
5/18                            1/9
Required ratio= 5:2
10. Two barrels conatin a mixture of ethanol and gasoline is 60%  in the first barrel and 30% in the second barrel .In what ratio must the mixtures from the first and the second barrels be taken to form a mixture containing 50% alcohol ?
A)  3:4
B)  5:8
C)  1:2
D)  5:4
E)  2 :1
Option E
Solution:
Mix. I                          Mix. II
3/5                              3/10
.                  1/2
1/5                                 1/10
Required ratio = 2 : 1

• A mixture of a certain quantity of milk with 15ltr of water is sold at 100 paisa per ltr. If pure milk be worth Rs 1.15ltr, then how much milk is there in the mixture?
A) 80ltr
B) 90ltr
C) 100ltr
D) 110ltr
E) 120ltr
Option C
Solution:

115………………0
.             100
100……………..15
20………………3
3= 15, 20 = 100
• In a mixture of 75ltr the ratio of milk to water is 2 : 1. The amount of water to be further added to the mixture so as to make the ratio of milk to water 1 : 2 will be?
A) 45
B) 60
C) 70
D) 75
E) 80
Option D
Solution:

.                        M : W
BEFORE       2   :   1…………..(1)
AFTER         1*2:   2*2
.                       2   :     4………….(2)
multiply 2 in equation (2) to make milk same……so…..1 =25
4 = 100
100 – 25 = 75ltr
• A container contained 60ltr milk. Out of this 6ltr of milk was taken out and replaced with water. This process was further repeated two times. How much milk is now in container?
A) 42.74
B) 43.74
C) 44.74
D) 45.74
E) 41.74
Option B
Solution:

.  6/60 = 1/10 = ( 1-1/10)T  = (9/10)³*T
729/1000*60 = 43.74ltr
• In an alloy zinc & copper are in the ratio of 1 :1. In the second alloy the same element are in the ratio 3 : 5. If these two alloys be mixed to form a new alloy in which two elements are in the ratio  2 : 3, find the ratio of these two alloys in the new alloy?
A) 2:3
B) 3:2
C) 1:4
D) 4:1
E) 3:1
Option C
Solution:

.               ½…………………..3/8
.                            2/5
.               1/40…………………1/10
.                   1         :             4
• In a class of 20 students the average of their marks is 59. If one student left the class then average become 60. Find the marks of that student?
A) 78
B) 59
C) 40
D) 30
E) 45
Option C
Solution:
Average increases by 1 when 1 leaves, so for 19 students::
.               59 – 19 = 40
• If the sum of 5 consecutive odd number is 265. Then the largest number would be?
A) 57
B) 59
C) 50
D) 40
E) 30
Option A
Solution:

.              Average = 265/5 = 53
(average)53…..55……57…….ans is 57
• In a bag there are three types of coins, 1rupee, 50paisa, 25paisa in the ratio of 5:10:16. The total value is Rs 700. The total number of coins is?
A) 1750
B) 1650
C) 1550
D) 1450
E) 1850
Option C
Solution:

.              5x : 10x : 16x
5x + 10x/2 + 16x/4 = 700
14x = 700
x = 50
(5x + 10x + 16x) = (5+10+16)*50 = 1550
• A can contain a mixture of two liquids P & Q in proportion 3 :5. When 8ltr of mixture are drawn off and the can is filled with Q, the proportion of P & Q becomes 3:7. How many ltr of liquid P was contained in the can initially?
A) 15ltr
B) 12ltr
C) 16ltr
D) 20ltr
E) 25ltr
Option A
Solution:

.                              P…………..Q
initial                      3…………….5
after                        3……………..7
7-5 = 2
2 =8
1 =4
after (7+3) =10= 40ltr
so initial = 3/3+5*40 = 15ltr
• 300 ltr of mixture contains 20% water in it and rest is milk. The amount of milk that must be added so that the resulting mixture contains 90% milk  is?
A) 200ltr
B) 300ltr
C) 250ltr
D) 350ltr
E) 400ltr
Option B
Solution:

.              20% of 300 = 60
now we have to make milk 90% then water will become 10%
10% = 60
100% = 600
so 600 – 300 = 300ltr
• 8kg of tea consisting Rs240 per kg is mixed with 9kg of tea costing Rs25o per kg. The average price per kg of the mixed tea is ?
A) 245.29
B) 246.29
C) 244.29
D) 247.29
E) 248.29
Option A
Solution:

.             8*240 + 9*250/17 = 4170/17
= 245.29