Top 100 Aptitude Questions and Answers for Competitive Exams

To find the percentage of students who failed in at least one subject (A or B or both), we can use the principle of inclusion-exclusion:

Percentage of students who failed in at least one subject (A or B or both) = Percentage of students who failed in M + Percentage of students who failed in E - Percentage of students who failed in both subjects

= M + E - B

= 34% + 42% - 20% = 76% - 20% = 56%

So, 56% of the students failed in at least one subject.

Now, to find the percentage of students who passed in both subjects, we subtract the percentage of students who failed in at least one subject from 100%:

Percentage of students who passed in both subjects = 100% - Percentage of students who failed in at least one subject = 100% - 56% = 44%

Therefore, the percentage of students who passed in both subjects is 44%.

To solve this problem, let's first represent the number of boys and girls in terms of a common variable. Let's say there are 3x boys and 2x girls.

Given that 20% of the boys and 25% of the girls are adults, we can calculate the number of adults among them.

Number of adult boys = 20% of 3x = (20/100) * 3x = 0.2 * 3x = 0.6x Number of adult girls = 25% of 2x = (25/100) * 2x = 0.25 * 2x = 0.5x

So, the total number of adult students = 0.6x (boys) + 0.5x (girls) = 1.1x

Now, the total number of students in the college = 3x (boys) + 2x (girls) = 5x

The percentage of students who are not adults = (Total number of non-adult students / Total number of students) * 100%

Since the total number of adult students is 1.1x, the total number of non-adult students = Total number of students - Total number of adult students = 5x - 1.1x = 3.9x

So, the percentage of students who are not adults = (3.9x / 5x) * 100% = (3.9/5) * 100% = 78%

Therefore, the percentage of students who are not adults is 78%.

To find the amount Imran borrowed, let's break down the problem step by step.

Let's denote the principal amount borrowed by Imran as P.

For the first four years, the simple interest is calculated at the rate of 8% per annum. So, the interest for the first four years = P * 8% * 4 = 0.08P * 4 = 0.32P

For the next six years, the simple interest is calculated at the rate of 10% per annum. So, the interest for the next six years = P * 10% * 6 = 0.1P * 6 = 0.6P

For the remaining five years (15 years total - 4 years - 6 years = 5 years), the simple interest is calculated at the rate of 12% per annum. So, the interest for the remaining five years = P * 12% * 5 = 0.12P * 5 = 0.6P

The total interest paid by Imran is given as Rs. 12,160.

So, adding up the interest for each period:

Total interest = 0.32P + 0.6P + 0.6P = 1.52P

Given that the total interest is Rs. 12,160, we can set up the equation:

1.52P = 12,160

Now, solve for P:

P = 12,160 / 1.52 P = 8,000

Therefore, Imran borrowed Rs. 8,000.

To calculate the percentage profit made by the bookseller, we use the formula:

Profit Percentage=(Selling Price−Cost PriceCost Price)×100%Profit Percentage=(Cost PriceSelling Price−Cost Price)×100%

Given: Cost Price (𝐶𝑃CP) = ₹110
Selling Price (𝑆𝑃SP) = ₹123.20

Using the formula:

Profit Percentage=(123.20−110110)×100%Profit Percentage=(110123.20−110)×100%

Profit Percentage=(13.20110)×100%Profit Percentage=(11013.20)×100%

Profit Percentage=(0.12)×100%Profit Percentage=(0.12)×100%

Profit Percentage=12%Profit Percentage=12%

So, the bookseller will make a profit of 12%.

To find the profit or loss percentage, we first need to calculate the cost price (CP) and the selling price (SP) of the bananas.

Given: Cost price of 6 bananas = ₹ 15 So, cost price of 1 banana = ₹ 15 / 6 = ₹ 2.50

Now, let's calculate the selling price: Selling price of 4 bananas = ₹ 12 So, selling price of 1 banana = ₹ 12 / 4 = ₹ 3.00

Now, we can compare the CP and SP to determine the profit or loss.

If SP > CP, it's a profit. If SP < CP, it's a loss.

Here, CP = ₹ 2.50 SP = ₹ 3.00

So, it's a profit of ₹ 0.50 per banana.

To find the profit percentage: Profit per banana / CP per banana * 100%

Profit per banana = ₹ 3.00 - ₹ 2.50 = ₹ 0.50

Profit percentage = (0.50 / 2.50) * 100% = 20%

Therefore, the fruit seller made a profit of 20%.

Let's denote the weight of A as 𝑥x kg and the weight of B as 𝑦y kg.

Given:

1. 𝑥+𝑦=80x+y=80 (Sum of weights of A and B is 80 kg)
2. 0.5𝑥=56𝑦0.5x=65y (50% of A's weight is 5665 times the weight of B)

We can solve these two equations to find the values of 𝑥x and 𝑦y, and then calculate the difference between their weights.

From equation 2: 0.5𝑥=56𝑦0.5x=65y Multiply both sides by 2 to get rid of the fraction: 𝑥=56𝑦×2x=65y×2 𝑥=106𝑦x=610y 𝑥=53𝑦x=35y

Now substitute this expression for 𝑥x into equation 1: 53𝑦+𝑦=8035y+y=80 83𝑦=8038y=80 Multiply both sides by 3883: 𝑦=80×38y=80×83 𝑦=30y=30

Now that we have found the weight of B, we can find the weight of A using equation 1: 𝑥+30=80x+30=80 𝑥=80−30x=80−30 𝑥=50x=50

So, the weight of A is 50 kg and the weight of B is 30 kg.

Now, let's find the difference between their weights: Difference=Weight of A−Weight of BDifference=Weight of A−Weight of B Difference=50−30Difference=50−30 Difference=20Difference=20

Therefore, the difference between their weights is 20 kg.

To solve this problem, let's denote:

• Initial price of sugar = P
• Initial quantity consumed = Q
• Initial expenditure = PQ

After the price increases by 15%, the new price becomes 1.15P.

To keep the expenditure constant, the new quantity consumed (let's call it Q') can be calculated using the formula:

New expenditure = New price × New quantity

Setting the new expenditure equal to the initial expenditure:

PQ = (1.15P) * Q'

Now, solve for Q':

Q' = PQ / (1.15P)

Simplify:

Q' = Q / 1.15

Now, let's find the percentage decrease in consumption:

Percentage decrease = [(Q - Q') / Q] * 100

Substituting the value of Q':

Percentage decrease = [(Q - (Q / 1.15)) / Q] * 100

Percentage decrease = [(Q * (1 - 1/1.15)) / Q] * 100

Percentage decrease ≈ [(1 - 0.8696) * 100] ≈ 13.04%

Therefore, the consumption of sugar should be decreased by approximately 13.04% to keep the expenditure on the purchase of sugar the same after a 15% increase in price.