# FREE Banking Exam Quantitative Aptitude Question and Answers

#### 474, 486, 510, 546,?

Let's find the pattern in the given sequence: 474 + 12 = 486 486 + 24 = 510 510 + 36 = 546 546 + 48 = 594 So, the next number in the sequence should be 594

#### For Rs 2250, P, Q, and R rent a penthouse. If they occupied it for 8, 10, and 12 hours, respectively, R will have to pay the following rent:

Let's assume that R's rent for 12 hours is Rs. X. Now, let's calculate the proportions of rent for each person based on the hours they used: P's proportion: 8 hours / (8 hours + 10 hours + 12 hours) = 8/30 Q's proportion: 10 hours / (8 hours + 10 hours + 12 hours) = 10/30 R's proportion: 12 hours / (8 hours + 10 hours + 12 hours) = 12/30 Given that they all together paid Rs. 2250 for the penthouse, we can set up the equation: P's rent + Q's rent + R's rent = Rs. 2250 (P's proportion) * Total Rent + (Q's proportion) * Total Rent + (R's proportion) * Total Rent = Rs. 2250 (8/30) * Total Rent + (10/30) * Total Rent + (12/30) * Total Rent = Rs. 2250 Now, we can simplify the equation: (30/30) * Total Rent = Rs. 2250 Total Rent = Rs. 2250 Now, let's find the rent paid by R for 12 hours: R's rent = (R's proportion) * Total Rent = (12/30) * Rs. 2250 = Rs. 900 So, the rent paid by R for 12 hours is Rs. 900.

#### With respective investments of Rs. 30,000 and Rs. 45, 000, Mae and Kumari launched a business. What percentage of the earnings of Rs. 1,50,00,000 will belong to Kumari after two years?

Given: Mae's investment = Rs. 30,000 Kumari's investment = Rs. 45,000 Total earnings after two years = Rs. 1,50,00,000 Step 1: Calculate the total investment: Total investment = Mae's investment + Kumari's investment Total investment = Rs. 30,000 + Rs. 45,000 Total investment = Rs. 75,000 Step 2: Calculate the ratio of Kumari's investment to the total investment: Kumari's ratio = Kumari's investment / Total investment Kumari's ratio = Rs. 45,000 / Rs. 75,000 Kumari's ratio = 3/5 Step 3: Calculate Kumari's share of the earnings: Kumari's share = Kumari's ratio * Total earnings Kumari's share = (3/5) * Rs. 1,50,00,000 Kumari's share = Rs. 90,00,000

#### 9, 43, 212, 1056, ?

If we look at the differences between consecutive terms: 43 - 9 = 34 212 - 43 = 169 1056 - 212 = 844 The differences between consecutive terms do not follow a simple pattern. However, let's look at the second differences: 169 - 34 = 135 844 - 169 = 675 The second differences are not constant either. But if we look closer, we can observe that the second differences are following a pattern: they are increasing by a factor of 5. So, to find the next second difference: 675 * 5 = 3375 Now, let's add this second difference to the last term in the sequence: 1056 + 3375 = 4431 So, the next term in the sequence should be 4431. The complete sequence is: 9, 43, 212, 1056, 4431, 5275

#### A man bought two different types of alcoholic beverages. The alcohol to water ratio in the first mixture is 4:5, whereas it is 6:7 in the second. If he combines the two provided mixtures to create a third combination of 22 litres with a 5:6 alcohol to water ratio, the amount of the first mixture needed to create the third kind of mixture is.

Step 1: Write down the ratios for each mixture: Mixture 1 (4:5) contains x liters of alcohol and (x + 22) liters of water. Mixture 2 (6:7) contains (22 - x) liters of alcohol and [(22 - x) + 22] liters of water. Step 2: Write down the ratio for the desired mixture (5:6): Desired Mixture (5:6) contains 5 liters of alcohol and 6 liters of water. Step 3: Set up the equation based on the alcohol content: Total alcohol in Mixture 1 + Total alcohol in Mixture 2 = Total alcohol in Desired Mixture [(4/9) * x] + [(6/13) * (22 - x)] = 5 Step 4: Solve for x: [(4/9) * x] + [(6/13) * (22 - x)] = 5 Multiply both sides by 117 to eliminate fractions: (13 * 4 * x) + (9 * 6 * (22 - x)) = 585 52x + 594 - 54x = 585 -2x = 585 - 594 -2x = -9 x = 9 So, 9 liters of the first mixture (with the alcohol to water ratio of 4:5) are needed to create the third combination. Therefore, the correct answer is 9 liters.

#### A dad and his son are typically 48 years old. 13 years ago, their ages were 11: 3 in proportion. What is the son's current age?

Step 1: Set up the equations based on the given information: The average age of the man and his son is 48 years: (M + S) / 2 = 48 The ratio of their ages 13 years ago was 11:3: (M - 13) / (S - 13) = 11/3 Step 2: Solve the equations simultaneously to find the values of M and S. From Equation 1, we can express M in terms of S: M + S = 96 M = 96 - S Now, substitute this value of M into Equation 2: (96 - S - 13) / (S - 13) = 11/3 Simplify the equation: (83 - S) / (S - 13) = 11/3 Cross-multiply: 3(83 - S) = 11(S - 13) Expand and solve for S: 249 - 3S = 11S - 143 Combine like terms: 14S = 392 Divide by 14: S = 392 / 14 S = 28 So, the present age of the son is 28 years.

#### The ratio of 15 to A to B is 10. B is 22 less than 3 times A if 10 is deducted from it. How much do A and B add up to?

15 times A is equal to 10 times B: 15A = 10B If 10 is subtracted from B, it is 22 less than 3 times A: B - 10 = 3A - 22 Now, let's solve these equations to find the values of A and B. From the first equation, we can express A in terms of B: A = (10/15)B A = (2/3)B Now, substitute this value of A into the second equation: B - 10 = 3((2/3)B) - 22 B - 10 = 2B - 22 B - 2B = -22 + 10 -B = -12 B = 12 Now, we can find the value of A using the first equation: A = (2/3) * 12 A = 8 The sum of A and B is: Sum = A + B Sum = 8 + 12 Sum = 20 Therefore, the sum of A and B is 20.

#### A tank can be filled by two pipelines in 20 and 24 hours, respectively. The tank can be emptied in 40 hours with a third pipe. if all three pipelines are operational and open at the same time. How long will it take the tank to fill up then?

Given: Pipe A can fill the tank in 20 hours. Pipe B can fill the tank in 24 hours. Pipe C can empty the tank in 40 hours. We've already calculated the rates: Pipe A's filling rate: 1 tank/20 hours = 1/20 tanks per hour. Pipe B's filling rate: 1 tank/24 hours = 1/24 tanks per hour. Pipe C's emptying rate: 1 tank/40 hours = -1/40 tanks per hour. When all three pipes are open and functioning simultaneously, their rates are additive: Total filling rate = (1/20) + (1/24) + (-1/40) tanks per hour = (12/240) + (10/240) - (6/240) tanks per hour = (22/240) - (6/240) tanks per hour = 16/240 tanks per hour = 1/15 tanks per hour The positive sign indicates that the tank is filling at a rate of 1/15 tanks per hour. To find how much time it takes to fill the tank, we can take the reciprocal of the total filling rate: Time to fill the tank = 1 / (1/15) hours = 15 hours

#### 17, 21, 37, 73, ?

The pattern in the given sequence is as follows: 17 (Prime) × 2 + 7 = 37 (Prime) 21 (Prime) × 2 - 5 = 37 (Prime) 37 (Prime) × 2 - 3 = 73 (Prime) 73 (Prime) × 2 + 1 = 147 (Not Prime) So, the next number in the sequence is 137 (Prime).

#### A salesman of fruits had some pineapples. He still has 350 pineapples after selling 30% of them. Initially, how many pineapples did he have?

Let's denote the original number of pineapples the fruit seller had as "P." According to the information given, the fruit seller sold 30% of the pineapples and still had 350 pineapples left. This can be represented by the equation: P - 0.30P = 350 Solving for P: 0.70P = 350 P = 350 / 0.70 P = 500 So, the fruit seller originally had 500 pineapples.

#### After two months, Mike joined Mich in his new venture. Mike spent $27,000 whereas Mich spent Rs. Their annual earnings totaled Rs. 5000. How much will Mich profit?

Given: Mike's investment = Rs. 27,000 Mich's investment = Rs. X (unknown) Total annual earnings = Rs. 5,000 Since Mike joined after two months, he was part of the venture for 10 months (2 months + 10 months = 12 months in a year). The ratio of Mike's investment to Mich's investment is: Mike's ratio = Mike's investment / Mich's investment Mike's ratio = Rs. 27,000 / X Total earnings after 12 months = Mike's profit + Mich's profit = Rs. 5,000 Now, we can set up an equation using the ratio: Mike's ratio + 1 = Total earnings / Mike's earnings Rs. 27,000 / X + 1 = Rs. 5,000 / Mike's profit Since we have the value of Mike's investment and total earnings, we can find Mike's profit: Mike's profit = Rs. 5,000 * (Rs. 27,000 / X + 1) Once we know Mike's profit, we can find Mich's profit using the total earnings: Mich's profit = Total earnings - Mike's profit Without knowing the exact value of Mich's investment (Rs. X), we cannot determine the exact profit for Mich. So, the correct answer from the provided options cannot be determined.

#### 450 kilometres are covered by a train in 6 hours. The speed of a bike is one-half that of a train. How long will it take the bike to travel 300 kilometers?

Let's first find the speed of the train. We know that the train covers 450 km in 6 hours. Speed of the train = Distance / Time = 450 km / 6 hours = 75 km/h Now, the speed of the bike is half of the speed of the train. Speed of the bike = (1/2) * Speed of the train = (1/2) * 75 km/h = 37.5 km/h Now, we can find the time taken by the bike to cover 300 km: Time = Distance / Speed = 300 km / 37.5 km/h = 8 hours So, the bike will take 8 hours to cover the distance of 300 km.

#### Sanjay made a $50,000 investment to launch a business. Ajay joined him with a contribution of Rs. 80,000 after six months. Sanjay added an additional sum of Rs. 20,000 after the business had been operating for a year. Three years later, they had a profit of Rs. 702,000. What portion of the profits goes to Sanjay ?

Given: Sanjay's initial investment = Rs. 50,000 Ajay's investment = Rs. 80,000 (after six months, which is equivalent to 0.5 years) Sanjay's additional investment after 1 year = Rs. 20,000 Total profit earned after 3 years = Rs. 7,02,000 First, let's calculate the total investment of Sanjay after 1 year: Sanjay's total investment after 1 year = Rs. 50,000 + Rs. 20,000 = Rs. 70,000 Next, let's adjust Ajay's investment for the same duration as Sanjay's total investment (3 years): Ajay's investment for 3 years = Rs. 80,000 * (3/2) = Rs. 1,20,000 Now, let's calculate the total investment: Total Investment = Sanjay's Investment + Ajay's Investment Total Investment = Rs. 70,000 + Rs. 1,20,000 Total Investment = Rs. 1,90,000 Next, we need to find the profit share of Sanjay based on his investment ratio: Sanjay's share = (Sanjay's Investment / Total Investment) * Total Profit Sanjay's share = (Rs. 70,000 / Rs. 1,90,000) * Rs. 7,02,000 Sanjay's share = (7/19) * Rs. 7,02,000 Sanjay's share = Rs. 2,58,000 So, the portion of the profits that goes to Sanjay is Rs. 2,58,000.

#### 73, 77, 85, 99, ?

To find the pattern in the given sequence (73, 77, 85, 99), let's examine the differences between consecutive terms: 77 - 73 = 4 85 - 77 = 8 99 - 85 = 14 The differences between consecutive terms are increasing by multiples of 4. To find the next difference: 14 + 4 = 18 Now, let's add this difference to the last term in the sequence: 99 + 18 = 117

#### Ali received a final grade of 35 in English, 39 in Science, 40 in Math, 37 in Hindi, and 32 in Social Studies. A student may earn a maximum of 60 points for each course. How much of a passing grade did Ali receive on this test?

To calculate Ali's overall passing grade, we need to find the average percentage of the grades he received in all subjects. Step 1: Find the total marks earned by Ali. Total marks earned = Marks in English + Marks in Science + Marks in Math + Marks in Hindi + Marks in Social Studies Total marks earned = 35 + 39 + 40 + 37 + 32 = 183 Step 2: Find the maximum marks possible. Maximum marks possible = Maximum marks per subject * Number of subjects Maximum marks possible = 60 * 5 = 300 Step 3: Calculate the percentage. Percentage = (Total marks earned / Maximum marks possible) * 100 Percentage = (183 / 300) * 100 Percentage = 0.61 * 100 Percentage = 61% So, Ali received a passing grade of 61% on this test.

#### 11, 18.5, 44.5, 141, ?

The pattern in the given sequence is as follows: 11 × 1.5 + 1 = 18.5 18.5 × 2.5 - 2 = 44.5 44.5 × 3.5 - 3 = 154.75 154.75 × 4.5 - 4 = 691.375 So, the next number in the sequence should be 691.375