Explanation

Discount = 450 - 369 = 81

Discount % = (81 / 450) × 100 = 18%

Explanation

Let's find the selling price (SP) after a 5% discount on the marked price (MP).

MP = Rs. 72,000

Discount = 5% of MP = 0.05 × 72,000 = Rs. 3,600

SP = MP - Discount = 72,000 - 3,600 = Rs. 68,400

The shopkeeper earned a 14% profit on the cost price (CP). Let's denote CP as x.

SP = CP + Profit

68,400 = x + 0.14x

68,400 = 1.14x

Now, find CP:

x = 68,400 / 1.14

x = 60,000

Explanation

To find the profit percentage:

Cost Price (CP) = 560

Selling Price (SP) = 600

Profit = SP - CP

= 600 - 560

= 40

Profit percentage = (Profit / CP) * 100

= (40 / 560) * 100

= 7.14%

Explanation

To find the markup (interest), we can use the formula:

Interest = Principal * Rate * Time

Given:

Principal = Rs. 45,000

Rate = 10% per annum = 0.10

Time = 73 days / 365 days (convert to years)

Time in years = 73/365

Interest = 45000 * 0.10 * (73/365)

= 45000 * 0.10 * 0.2

= 900

Explanation

Profit = Selling Price - Cost Price

= 540 - 470

= 70

Profit Percentage = (Profit ÷ Cost Price) × 100

= (70 ÷ 470) × 100

= 15 (14.89%)

Explanation

Given:

Selling price (SP) = Rs. 8413

Loss percentage = 6%

Let's denote the cost price as CP.

Since the shopkeeper loses 6%, the selling price is 94% of the cost price (100% - 6% = 94%).

SP = 0.94 × CP

8413 = 0.94 × CP

CP = 8413 / 0.94

CP = 8950

Explanation

The term "percent" comes from the Latin per centum, meaning "by the hundred."

So, 1% literally means 1 out of 100.

Explanation

To find the time it takes for the amount to reach Rs. 784:

Use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A = 784, P = 700, r = 4% = 0.04, n = 1 (compounded annually)

784 = 700(1 + 0.04/1)^(1t)

Divide both sides by 700:

1.1286 ≈ (1.04)^t

Take the logarithm of both sides:

t ≈ log(1.1286) / log(1.04)

≈ 3

So, it will take approximately:

3 years

Explanation

30% of 50 students = (30/100) × 50 = 15

So, 15 students received an A grade.

Explanation

Let's say the number of girls is x. Then, the number of boys is 2x (since there are twice as many boys as girls).

Total students = x (girls) + 2x (boys) = 3x

Now, let's calculate the number of students who failed:

Girls who failed = 45% of x = 0.45x

Boys who failed = 30% of 2x = 0.6x

Total students who failed = 0.45x + 0.6x = 1.05x

Now, let's calculate the number of students who passed:

Total students who passed = Total students - Total students who failed

= 3x - 1.05x

= 1.95x

Percentage of students who passed = (1.95x / 3x) × 100%

= 65%