Percentage Questions with Answers

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 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%.

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.