Ratio and Proportion: Bank Exam Practice Questions (SBI, IBPS, RRB, PO & Clerk)

Ans: A

Explanation: First, calculate A’s share: (2/3) * 50,000 = Rs. 33,333.33. Then, find the money left after A gets his share: 50,000 – 33,333.33 = Rs. 16,666.67. Next, calculate B’s share: (1/5) * 16,666.67 = Rs. 3,333.33. Now find the money left for C and D: 16,666.67 – 3,333.33 = Rs. 13,333.34. The ratio of C:D is 2:3, so C gets 2/(2+3) = 2/5 of the remaining money. C’s share is (2/5) * 13,333.34 = Rs. 5,333.33. This is approximately Rs. 5,334.

Correct Option: A

Ans: C

Explanation: Let the daughter’s current age be ‘d’ and the father’s current age be ‘f’. We are given:
f = d + 30 (Equation 1)
Fifteen years ago, the daughter’s age was (d-15) and the father’s age was (f-15).
(f-15) / (d-15) = 3/1 => f – 15 = 3(d – 15) => f – 15 = 3d – 45 => f = 3d – 30 (Equation 2)
Now we have two equations:
f = d + 30
f = 3d – 30
Since both are equal to f, we can equate them:
d + 30 = 3d – 30
60 = 2d
d = 30
Now find f:
f = d + 30 = 30 + 30 = 60
The combined current age is d + f = 30 + 60 = 90

Correct Option: C

Ans: B

Explanation: Let the initial amounts of milk and water be 8x and x liters respectively.
When 18 liters of the mixture are removed, the ratio of milk to water remains the same, 8:1. The fractions of milk and water in the mixture are 8/9 and 1/9.
The amount of milk removed = (8/9) * 18 = 16 liters.
The amount of water removed = (1/9) * 18 = 2 liters.
After removing 18 liters, the remaining milk = 8x – 16 liters.
Remaining water = x – 2 liters.
Then, 4 liters of water are added.
The new amount of milk = 8x – 16 liters.
The new amount of water = x – 2 + 4 = x + 2 liters.
According to the question, the new amount of milk is 24 liters greater than the amount of water.
So, 8x – 16 = x + 2 + 24
8x – 16 = x + 26
7x = 42
x = 6
Initial amount of milk = 8x = 8 * 6 = 48 liters.

Correct Option: B

Ans: D

Explanation: Let the first amount be x and the second amount be y. We know that x + y = 1176.
We are also given that (3/5)x / (2/7)y = 3/2. This can be rewritten as (3/5)x * (7/2y) = 3/2, or (21/10) * (x/y) = 3/2. Simplifying, x/y = (3/2) * (10/21) = 30/42 = 5/7. Therefore, x = (5/7)y.
Substitute x in the first equation, we get (5/7)y + y = 1176, or (12/7)y = 1176. Thus, y = 1176 * (7/12) = 686.
Since x + y = 1176 and y = 686, then x = 1176 – 686 = 490.
Correct Option: D

Ans: D

Explanation:
1. Find E’s age: The ratio of E and F’s ages is 7:3, and F is 21. So, 3 parts represent 21 years. Therefore, one part is 21/3 = 7 years. E’s age is 7 parts, so E is 7 * 7 = 49 years old.
2. Find D’s age: D is 5 years younger than E. Therefore, D is 49 – 5 = 44 years old.

Ans: A

Explanation: Let A’s age five years ago be 3x and B’s age five years ago be 2x.
Then, A’s present age is 3x + 5 and B’s present age is 2x + 5.
Five years from now, A’s age will be 3x + 5 + 5 = 3x + 10 and B’s age will be 2x + 5 + 5 = 2x + 10.
The ratio of their ages five years from now is 4:3.
So, (3x + 10) / (2x + 10) = 4/3
3(3x + 10) = 4(2x + 10)
9x + 30 = 8x + 40
x = 10
A’s present age = 3x + 5 = 3(10) + 5 = 35 years
B’s present age = 2x + 5 = 2(10) + 5 = 25 years
The sum of their present ages = 35 + 25 = 60 years.

Ans: D

Explanation:
Let Raghu’s age be R, Vibhu’s age be V, and Sidhu’s age be S.
From the first ratio, R/V = 3/4, so V = (4/3)R.
From the second ratio, R/S = 7/6, so S = (6/7)R.
We are given that R = S + 9.
Substitute S = (6/7)R into the equation R = S + 9:
R = (6/7)R + 9
R – (6/7)R = 9
(1/7)R = 9
R = 63
Now, find V: V = (4/3) * 63 = 84
Now, find S: S = (6/7) * 63 = 54
The combined age is R + V + S = 63 + 84 + 54 = 201

Correct Option: D

Ans: C

Explanation: Let the initial number of balls Rinku, Puneet, and Sweety have be 7x, 6x, and 9x respectively. After Sweety gives 15 balls to Rinku, Rinku has 7x + 15 balls, Sweety has 9x – 15 balls, and Puneet still has 6x balls. The new ratio is 5:3:3. Therefore:

(7x + 15) / 6x = 5/3
3(7x + 15) = 5(6x)
21x + 45 = 30x
9x = 45
x = 5

The initial number of balls Rinku possessed is 7x = 7 * 5 = 35.

Correct Option: C

Ans: C

Explanation: Let Riya’s monthly salary be ‘x’.
Rent = 20% of x = 0.2x
Money after rent = x – 0.2x = 0.8x
Money after flight = 0.8x – 5000
Let the insurance premium be ‘i’ and savings be ‘s’.
i:s = 3:2. Therefore i = (3/2)s
Insurance + Savings = 0.8x – 5000 => i + s = 0.8x – 5000
Also, rent payment is Rs. 4000 less than the insurance premium, i.e., 0.2x = i – 4000 => i = 0.2x + 4000
Substitute i in i + s = 0.8x – 5000
0.2x + 4000 + s = 0.8x – 5000
s = 0.6x – 9000
Substitute s in i = (3/2)s => i = (3/2)*(0.6x – 9000) = 0.9x – 13500
Now equate i from both i = 0.2x + 4000 and i = 0.9x – 13500
0.2x + 4000 = 0.9x – 13500
0.7x = 17500
x = 17500 / 0.7 = 25000
Therefore, Riya’s monthly salary is Rs. 25000.

Correct Option: C

Ans: C

Explanation: Let’s use variables:
* R = Rohan’s current age
* G = Gaurav’s current age
* K = Ratika’s current age

From the problem, we can derive these equations:
1. R = G + 1 (Rohan is a year older than Gaurav)
2. R + G = K + 2 (Combined age of Rohan and Gaurav is two years greater than Ratika’s)
3. (R + 9) / (K + 9) = 4/5 (In nine years, the ratio of Rohan’s age to Ratika’s age will be 4:5)

Substitute equation (1) into equation (2):
(G + 1) + G = K + 2
2G + 1 = K + 2
K = 2G – 1

Substitute equation (1) into equation (3):
((G + 1) + 9) / (K + 9) = 4/5
(G + 10) / (K + 9) = 4/5
5(G + 10) = 4(K + 9)
5G + 50 = 4K + 36
5G – 4K = -14

Substitute K = 2G – 1 into 5G – 4K = -14:
5G – 4(2G – 1) = -14
5G – 8G + 4 = -14
-3G = -18
G = 6

Now we can find other ages:
R = G + 1 = 6 + 1 = 7
K = 2G – 1 = 2(6) – 1 = 11

Ratika’s age in three years = K + 3 = 11 + 3 = 14

Correct Option: C

Ans: C

Explanation: Let Rohit’s income be 5x and Ravi’s income be 4x. Let Rohit’s expenses be 6y and Ravi’s expenses be 5y. Their savings are in a 3:2 ratio, and they save a combined total of Rs. 5000. So, Rohit’s savings are 3k and Ravi’s savings are 2k, and 3k + 2k = 5000, which means 5k = 5000, thus k = 1000. Therefore, Rohit saves 3 * 1000 = 3000 and Ravi saves 2 * 1000 = 2000.

Savings = Income – Expenses.
For Rohit: 3000 = 5x – 6y
For Ravi: 2000 = 4x – 5y

Multiplying Rohit’s equation by 5 and Ravi’s equation by 6:
15000 = 25x – 30y
12000 = 24x – 30y

Subtracting the second equation from the first:
3000 = x
So, Rohit’s income = 5x = 5 * 3000 = 15000 per month.
Rohit’s earnings for six months = 15000 * 6 = 90000

Correct Option: C

Ans: C

Explanation: Let Shailesh’s current age be 14x and Ramesh’s current age be 17x. In six years, Shailesh’s age will be 14x + 6 and Ramesh’s age will be 17x + 6. We are given that in six years, their ages will be proportional to 17:20. Therefore, (14x + 6) / (17x + 6) = 17 / 20. Cross-multiplying, we get 20(14x + 6) = 17(17x + 6). This simplifies to 280x + 120 = 289x + 102. Subtracting 280x from both sides gives 120 = 9x + 102. Subtracting 102 from both sides gives 18 = 9x. Dividing both sides by 9, we find x = 2. Ramesh’s current age is 17x = 17 * 2 = 34 years.
Correct Option: C

Ans: C

Explanation: The ratio of John’s savings to Mary’s savings is 5:7. This means that for every $5 John saves, Mary saves $7. We know John saved $250. Let Mary’s savings be represented by ‘x’. We can set up a proportion: 5/7 = 250/x. To solve for x, we cross-multiply: 5 * x = 7 * 250. This simplifies to 5x = 1750. Dividing both sides by 5 gives x = 350.

Ans: B

Explanation: Let the present ages of A and B be 5x and 3x respectively.
Five years ago, their ages were (5x-5) and (3x-5).
According to the problem, (5x-5)/(3x-5) = 2/1.
Cross-multiplying, 5x-5 = 6x-10.
Therefore, x = 5.
Present age of A = 5x = 5*5 = 25 years.
Present age of B = 3x = 3*5 = 15 years.
Age of A after 10 years = 25+10 = 35 years.
Age of B after 15 years = 15+15 = 30 years.
Quantity A = 35
Quantity B = 30
Therefore, Quantity A > Quantity B.

Ans: E

Explanation: Let the number of men be 7x and the number of women be 5x. We are given that 7x = 350. Solving for x, we get x = 350/7 = 50. Therefore, the initial number of women is 5x = 5 * 50 = 250.

To make the ratio 1:1, the number of women must equal the number of men, which is 350. So, the number of women that need to be hired is 350 – 250 = 100.

Ans: E

Explanation: Let’s assume the total number of visitors for clubs A, B, and C are 10x, 12x, and 9x respectively.

Club A:
– Male visitors: 35% of 10x = 3.5x
– Female visitors: 65% of 10x = 6.5x

Club B:
– Male visitors: 45% of 12x = 5.4x
– Female visitors: 55% of 12x = 6.6x

Club C:
– Male visitors: 40% of 9x = 3.6x
– Female visitors: 60% of 9x = 5.4x

Total Male visitors: 3.5x + 5.4x + 3.6x = 12.5x
Total Female visitors: 6.5x + 6.6x + 5.4x = 18.5x

Ratio of male to female visitors: 12.5x : 18.5x = 12.5 : 18.5 = 125 : 185 = 25 : 37

Correct Option: E

Ans: C

Explanation:
Let A’s income be 7x and B’s income be 9x.
Let A’s savings be 2y and B’s savings be 3y.
2y + 3y = 10000 => 5y = 10000 => y = 2000
A’s savings = 2 * 2000 = 4000
B’s savings = 3 * 2000 = 6000
A’s spending = 7x – 4000
B’s spending = 9x – 6000
B’s spending is 25% higher than A’s, so:
9x – 6000 = 1.25 * (7x – 4000)
9x – 6000 = 8.75x – 5000
0.25x = 1000
x = 4000
A’s income = 7 * 4000 = 28000
B’s income = 9 * 4000 = 36000
Combined income = 28000 + 36000 = 64000

Correct Option: C

Ans: A

Explanation: Let the two numbers be 21x and 26x. When 8 is added to both, the new numbers are 21x + 8 and 26x + 8. The new ratio is given as 5:6. Therefore, (21x + 8) / (26x + 8) = 5/6. Cross-multiplying gives 6(21x + 8) = 5(26x + 8), which simplifies to 126x + 48 = 130x + 40. This simplifies to 4x = 8, so x = 2. The original numbers are 21*2 = 42 and 26*2 = 52. If we subtract 4 from both, the new numbers are 42 – 4 = 38 and 52 – 4 = 48. The ratio of the new numbers is 38:48, which simplifies to 19:24.

Correct Option: A