Ratio And Proportion Questions For IBPS RRB PO

Download Top-20 IBPS RRB PO Ratio and Proportion Questions PDF. Ratio and Proportion questions based on asked questions in previous year exam papers very important for the IBPS RRB PO (Officer Scale-I, II & III) exam.

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Question 1: A solution contains 3 liquids A,B and C.The ratio of volumes of B and C is 7:2.It contains 15 litres of A.If 5 litres of B and 4 litres of C is replaced by equal volumes of A then the ratio of volumes of A and B becomes 4:5. What is the total volume of the solution?

a) 60 litres

b) 50 litres

c) 45 litres

d) 30 litres

e) 70 litres

Question 2: How many kilograms of white rice costing Rs 30 per kg should be mixed with 42 kgs plain rice costing Rs 20 per kg so that he gets 50% profit on selling it at Rs 34.50 per kilogram ?

a) 12 kgs

b) 15 kgs

c) 18 kgs

d) 21 kgs

e) 24 kgs

Question 3: If ‘x’ litres of pure milk is added to a solution of 40 litres containing milk to water in the ratio of 3:5 to make the ratio 1:1 then what will be the ratio of water to milk if ’2x’ of water is added to the final solution formed ?

a) 12:7

b) 9:4

c) 7:4

d) 4:7

e) 4:9

Question 4: A 55 litre solution contains water and milk in the ratio of 3:8 and ‘x’ litres of either milk or water is added to the solution so that the ratio of water to milk becomes 3:2 and if ‘x’ litres of same type is added to the solution then what is the ratio of water to milk in the resulting ratio ?

a) 4:3

b) 8:19

c) 8:21

d) 21:8

e) 19:8

Question 5: Ram purchased three variety of barley at Rs. 100 per kg, Rs. 140 per kg and Rs. 180 per kg respectively. In what ratio he should mix these three varieties in that order so that the average cost of the mixture is Rs. 150 per kg?

a) 2 : 4 : 7

b) 1 : 5 : 10

c) 1 : 2 : 3

d) 2 : 5 : 5

e) None of the above

Question 6: Ram mixes acid and water in 3:5 to get solution X whereas he mixes water and acid in 2:3 to get solution Y. In what ratio he should mix solution X and Y to make another solution which contains 50% acid?

a) 3 : 5

b) 4 : 5

c) 5 : 4

d) 5 : 3

e) 1 : 1

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Question 7: Jar A contains 70% milk and the rest is water whereas Jar B contains 60% water and the rest is milk. How many liters of solution A should be mixed with 100 liters of solution B to make 50% water-milk solution?

a) 20

b) 100

c) 80

d) 40

e) 50

Question 8: A milkman mixed water in the pure milk in the ratio of 2 : 3. If water is available at one-sixth of the price of pure milk then find out the profit percentage made by the milkman when he sold the entire mixture at the cost price of pure milk?

a) 25 percent

b) 33.33 percent

c) 50 percent

d) 40 percent

e) 66.66 percent

Question 9: Two varieties of rice cost Rs. 40 and Rs. 60 per kg. Another two varieties Haffa and Jaffa are created by mixing the first two varieties in 2:3 and 3:1 ratio. Find out the difference between the cost price of Haffa and Jaffa?

a) Rs. 5 per kg

b) Rs. 4 per kg

c) Rs. 6 per kg

d) Rs. 7 per kg

e) None of the above

Question 10: A solution containing alcohol and water in the ratio 7 : 2 is mixed with twice the amount of another solution containing alcohol and water in the ratio 5 : 1. What is the percentage of alcohol in the final mixture?

a) 78.91%

b) 90%

c) 75.12%

d) 79.38%

e) 81.48%

Question 11: Two varieties of rice A and B are mixed in the ratio 4 : 5 to form a mixture X and in the ratio 3 : 4 to form another mixture Y. When X and Y are mixed in equal quantities, a new mixture Z is formed. When 3 kg of rice A is mixed in Z, the ratio of both the varieties of rice in Z becomes equal. What was the quantity of X and Y mixed to form Z?

a) 11.8125 kg

b) 13.225 kg

c) 18 kg

d) 19.75 kg

e) 10.1125 kg

Question 12: A solution containing milk and water in the ratio 3 : 1 is mixed with twice the amount of another solution containing milk and water in the ratio 2 : 1. What is the percentage of milk in the final mixture?

a) 77.11%

b) 69.44%

c) 57.2%

d) 56%

e) 60.36%

Question 13: A solution containing milk and water in the ratio 5 : 1 is mixed with 20 litres of milk. After removing 10.7 litres of the new mixture, the ratio of water and milk in the remaining mixture is found to be 3 : 25. What was the initial quantity of mixture?

a) 23.4 litres

b) 36 litres

c) 30.6 litres

d) 24 litres

e) 21.6 litres

Question 14: A milkman has some quantity of milk with him. He sells 20% of the milk and replaces it water. He realized that the mixture is too dilute and hence, he adds 20L of pure milk to the mixture. He then again sells 40% of the mixture and replaces it water. He adds 48L of pure milk to the mixture. If he now has 300L of pure milk with him then what is the quantity of the milk with which he started?

a) 520L

b) 550L

c) 500L

d) 480L

e) 450L

Question 15: The cost of two different varieties of rice A and B Rs. 40/kg and Rs. 60/kg respectively. If A and B are mixed together in the ratio of 5 : 7 what will be the total cost of the mixture?

a) Rs. $\frac{155}{3}$/kg

b) Rs. 50/kg

c) Rs. 80/kg

d) Rs. 53/kg

e) Cannot be determined

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Question 16: The cost of three different varieties of milk A, B, and C is Rs. 20/litre, Rs. 25/litre and Rs. 30/litre respectively. If A, B and C are mixed together in the ratio of 2 : 1 : 3, what will be the total cost of the mixture?

a) Rs. $\frac{155}{6}$/litre

b) Rs. 25/litre

c) Rs. $\frac{155}{12}$/litre

d) Rs. 29/litre

e) Cannot be determined

Question 17: The cost of three different varieties of rice A, B, and C is Rs. 20/kg, Rs. 25/kg and Rs. 30/kg respectively. If A, B and C are mixed together in the ratio of 2 : 1 : 2, what will be the cost of the mixture per kg?

a) Rs. 75

b) Rs. 25

c) Rs. 30

d) Rs. 125

e) Rs. 100

Question 18: A mixture contains water and milk in the ratio of 3 : 5. If 4 litres of water and 5 litres of milk are added to the mixture, the ratio of water and milk becomes 2 : 3. What is the quantity of water in the final mixture?

a) 11 litres

b) 12 litres

c) 8 litres

d) 10 litres

e) 9 litres

Question 19: A mixture contains water and alcohol in the ratio of 5 : 2. If 5 litres of water and 4 litres of alcohol are added to the mixture, the ratio of water and alcohol becomes 2 : 1. What is the quantity of alcohol in the final mixture?

a) 10 litres

b) 7 litres

c) 8 litres

d) 12 litres

e) Cannot be determined

Question 20: A mixture A contains milk and water in the ratio of 7 : 2. Another mixture B contains milk and water in the ratio of 2 : 1. If A and B are mixed in the ratio of 1 : 3, what is the ratio of milk and water in the final mixture?

a) 12 : 7

b) 23 : 17

c) 25 : 11

d) 29 : 11

e) 13 : 5

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Answers & Solutions:

1) Answer (A)

Let the initial volumes be A,B and C
A=15 litres
B=7x and C=2x
A=15+5+4=24 litres
B=7x-5
C=2x-4
Given 24/(7x-5)=4:5
120=28x-20
28x=1440
x=5 litres
B=7(5)-5=30 litres
C=2(5)-4=6 litres
Total volume=24+30+6=60 litres

2) Answer (C)

Given profit percent=50
Selling price=34.50
SP=1.5 *CP
34.50=1.5*CP
CP=34.5/1.5
CP=Rs 23
let the ratio of number of kg’s of white rice to plain rice be x
By applying the rule of allegations we have
x=(23-20)/(30-23)
x=3:7
So 42 kgs of plain rice is added and let ‘y’ kgs of white rice be added
Therefore 3/7 =y/42
y=3*6
y=18 kgs

3) Answer (B)

In the given solution quantity of milk=(3/8)*40 =15 litres
Quantity of water=(5/8)*40=25 litres
Given x litres of milk is added and so
(15+x)/(25) =1/1
15+x=25
x=10 litres
Now 2x=20 litres of water is added to the final solution
i.e water =25 +20
=45 litres
Milk=15+10=25 litres
ratio=45:20
=9:4

4) Answer (D)

Since the ratio in the resulting mixture in case 1 has water in greater quantity the solution that is added should definitely be water and so
Given solution has (3/11)*55=15 litres of water
(8/11)*55=40 litres of milk
‘X’ litres of water is added to it
Therefore (15+x)/(40)=3:2
30+2x=120
2x=90
x=45 litres
And then again 45 litres of water is added to the solution and so total water in the solution =60+45=105 litres
milk=40 litres
Ratio of water to milk=105:40
=21:8

5) Answer (D)

Let us check the options.
Option (A): Average cost price of the mixture = $\dfrac{200+560+1260}{2+4+7}$ = Rs. 155.38
Option (B): Average cost price of the mixture = $\dfrac{100+700+1800}{1+5+10}$ = Rs. 162.50
Option (C): Average cost price of the mixture = $\dfrac{100+280+540}{1+2+3}$ = Rs. 153.33
Option (D): Average cost price of the mixture = $\dfrac{200+700+900}{2+5+5}$ = Rs. 150
Therefore, option D is the correct answer.

6) Answer (B)

Let ‘a’ and ‘b’ be the quantity of solution X and Y mixed by Ram. It is given that the solution contains 50% acid hence,
$\Rightarrow$ $\dfrac{\dfrac{3a}{8}+\dfrac{3b}{5}}{a+b} = \dfrac{50}{100}$

$\Rightarrow$ $\dfrac{15a+24b}{40(a+b)} = \dfrac{1}{2}$

$\Rightarrow$ $30a+48b = 40a+40b$

$\Rightarrow$ $\dfrac{a}{b} = \dfrac{4}{5}$

Hence, option B is the correct answer.

7) Answer (E)

Let ‘X’ liters of solution A is mixed with 100 liters of solution B.
Concentration of milk in solution B = 100 – 60 = 40%.
The resultant solution is a 50% water-milk solution.
Hence,
$\dfrac{0.70*X + 0.40*100}{X+100} = \dfrac{50}{100}$
$70*X + 4000 = 50*X + 5000$
$20X= 1000$
$X= 50$liters.
Hence, option E is the correct answer.

8) Answer (C)

Let ‘$\text{P}$’ be the cost price of pure milk per liter. Therefore, cost price of water = $\dfrac{\text{P}}{6}$.
Let us assume that milkman mixed $\text{2L}$ and $\text{3L}$ volume of water and pure milk.
Hence, total cost incurred by the milkman = $2\text{L}*\dfrac{\text{P}}{6} + 3\text{L*P}$ = $\dfrac{10\text{LP}}{3}$
Profit made by the milkman in the transaction = $5\text{L*P} – \dfrac{10\text{LP}}{3}$ = $\dfrac{5\text{LP}}{3}$
Therefore, the profit percentage made by the milkman = $\dfrac{\dfrac{5\text{LP}}{3}}{\dfrac{10\text{LP}}{3}}\times 100$ = 50 percent.
Therefore, option C is the correct answer.

9) Answer (D)

Cost price of Haffa per kg = $\frac{2*40+3*60}{2+3}$ = Rs. 52 per kg.

Cost price of Jaffa per kg = $\frac{3*40+1*60}{3+1}$ = Rs. 45 per kg.

Hence, the difference between the cost price of Haffa and Jaffa = 52 – 45 = Rs. 7 per kg.
Therefore, option D is the correct answer.

10) Answer (E)

Let 9 litres of the first solution be mixed with 18 litres of the second solution.
Therefore, total volume of the solution = (9 + 18) litres = 27 litres
Quantity of alcohol in the first solution = $\frac{7}{9} * 9$ litres = 7 litres
Quantity of alcohol in the second solution = $\frac{5}{6} * 18$ litres = 15 litres
Total quantity of alcohol = (7 + 15) litres = 22 litres
% of milk = $\frac{22}{27} * 100$% = 81.48%
Hence, option E is the correct answer.

11) Answer (A)

Let there be 4k kg of rice A and 5k kg of rice B in mixture X and
let there be 3m kg of rice A and 4m kg of rice B in mixture Y
Total quantity of X = (4k + 5k) kg = 9k kg
Total quantity of Y = (3m + 4m) kg = 7m kg
When X and Y are mixed in equal quantities to form Z,
Quantity of rice A in Z = (4k + 3m) kg
Quantity of rice B in Z = (5k + 4m) kg
It is given that, 4k + 3m + 3 = 5k + 4m
or, k + m = 3……………(i)
Also, Quantity of X = Quantity of Y
=> 9k = 7m…………….(ii)
On solving (i) and (ii), we get
k = $\dfrac{21}{16}$ and m = $\dfrac{27}{16}$
Quantity of X and Y mixed = 9k or 7m = 11.8125 kg
Hence, option A is the correct answer.

12) Answer (B)

Let 12 litres of the first solution be mixed with 24 litres of the second solution.
Therefore, total volume of the solution = (12 + 24) litres = 36 litres
Quantity of milk in the first solution = $\frac{3}{4} * 12$ litres = 9 litres
Quantity of milk in the second solution = $\frac{2}{3} * 24$ litres = 16 litres
Total quantity of milk = (9 + 16) litres = 25 litres
% of milk = $\frac{25}{36} * 100$% = 69.44%

13) Answer (B)

Let the milk and water in the original mixture be 5$k$ and $k$.
After adding 20 litres of milk, the ratio of milk and water changed to 25 : 3
(Removing 10.7 litres of the mixture is irrelevant as it will not change the ratio of milk and water in the mixture)
So, $\frac{5k + 20}{k} = \frac{25}{3}$
On solving, we get $k$ = 6
Total volume of the initial mixture = $5k + k$ = 36 litres
Hence, option B is the correct answer.

14) Answer (C)

Let the quantity of milk with the milkman be xL. He sells 20% of it and thus he is left with 0.8x.
He adds 20L of pure milk and thus. he now has 0.8x+20 L of milk with him.
Out of this he sells 40% of the milk.
He is now left with (0.8x+20)*0.6 = 0.48x+12 L of milk.
He adds 48L of pure milk and he now has 0.48x+12+48 = 0.48x+60 L of milk.
Given, 0.48x+60 = 300
Thus, x = 240/0.48 = 500L
Hence, option C is the correct answer.

15) Answer (E)

As the total quantity of the mixture is not known, we cannot calculate the total cost of the mixture.
Hence, option E is the correct answer.

16) Answer (E)

As the total quantity of the mixture is not known, we cannot calculate the total cost of the mixture.
Hence, option E is the correct answer.

17) Answer (B)

Let 2 kg of A, 1 kg of B and 2 kg of C are mixed together.
Total rice = (2 + 1 + 2) kg = 5 kg
Cost of A in the mixture = Rs. (2 * 20) = Rs. 40
Cost of B in the mixture = Rs. (1 * 25) = Rs. 25
Cost of C in the mixture = Rs. (2 * 30) = Rs. 60
Total cost of the mixture = Rs. (40 + 25 + 60) = Rs. 125
Cost per kg = Rs. $\frac{125}{5}$ = Rs. 25
Hence, option B is the correct answer.

18) Answer (D)

Let the quantity of water and milk be $3x$ and $5x$
It is given that, $\frac{3x + 4}{5x + 5} = \frac{2}{3}$
On solving, we get $x$ = 2
Therefore, the quantity of water in the final mixture = (3 * 2 + 4) litres = 10 litres.
Hence, option D is the correct answer.

19) Answer (A)

Let the quantity of water and alcohol be $5x$ and $2x$
It is given that, $\frac{5x + 5}{2x + 4} = \frac{2}{1}$
On solving, we get $x$ = 3
Therefore, the quantity of alcohol in the final mixture = (3 * 2 + 4) litres = 10 litres.
Hence, option A is the correct answer.

20) Answer (C)

As A and B are mixed in the ratio of 1 : 3, let us assume that 9 litres of A and 27 litres of B are mixed.
In 9 litres of A, milk is 7 litres, and water is 2 litres.
In 27 litres of B, milk is 18 litres, and water is 9 litres.
When A and B are mixed, quantity of milk = (7 + 18) litres = 25 litres
When A and B are mixed, quantity of water = (2 + 9) litres = 11 litres
Required ratio is 25 : 11
Hence, option C is the correct answer.

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