The average marks of 28 students in Mathematics was 50. 8 students left the school and then the average increased by 5. What is the average of marks obtained by the students who left the school?

Explanation
Total marks of 28 students in Mathematics = 28 x 50 = 1400 New number of students = 28 - 8 = 20 New average of marks in Mathematics = 50 + 5 = 55 ∴ Total marks of 20 students in Mathematics = 20 x 55 = 1100 ∴ Total marks of 8 students who left the school = 1400 - 1100 = 300 ∴ Average marks of these 8 students =  300/8 = 37.5

Explanation
For one digit number 1 to 9 →1 × 9 = 9 For two digit number 10 to 99 → 2 × 90 = 180 For three digit number 100 to 300 →3 × 201 = 603 Hence, total number of required digits = 9 + 180 + 603  =  792

Explanation

Explanation
A complete day i.e 24 hours is 100%. 24 hours = 24 × 60 minutes = 1440 mins 4 hours, 30 mins = 270 mins 1440 mins = 100% of the day 270 mins = ? = 270 × 100 / 1440 = 18.75% 4 hours and 30 minutes is 18.75% of a day.

Explanation
Total age of new players = Total age of replaced players - Total decrease in age of all players  Total age of new players = 17 + 20 - (11 × 2)/12 ⇒ Total age of new players = 37 - (11/6) ⇒ Total age of new players = (222 - 11)/6 ⇒ Total age of new players = 211/6 ⇒ The Average age of two new players = 211/12 ∴ The average age of two new players is 17 years 7 months.

Explanation
The result of the expression 4 3 − 4 2 2 2 4^3 - frac{4^2}{2^2} ​ is 60. ​

Explanation
Paid= 3/5 Remaining = 1 – 3/5 = 2/5 Given conditions : 2/5 x Total amount = 400 ⇒        Total amount = 1000

Explanation
Let the two numbers be x and y. Given: x + y = 2490 ... (Equation 1) Also, 6.5% of x = 8.5% of y To simplify, convert percentages to decimals : 0.065x = 0.085y Now, divide both sides by 0.065: x = (0.085/0.065)y x = (85/65)y x = (17/13)y ... (Equation 2) Now, substitute Equation 2 into Equation 1: (17/13)y + y = 2490 Combine like terms: (30/13)y = 2490 Multiply both sides by 13/30: y = 1079 Now that we have found y, we can find x: x = 2490 - y (from Equation 1) x = 2490 - 1079 x = 1411 So, the correct answer is: 1411, 1079

Explanation
Let the total distance be x km . The man covers half the distance at 6 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 6 = x/12 The man covers the remaining half at 3 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 3 = x/6 The total time taken to cover the entire distance is the sum of the times taken to cover each half : Total Time = x/12 + x/6 To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as: Total Time = x/12 + 2x/12 = 3x/12 = x/4 Now, we can find the average speed: Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr So, the correct answer is: 4 km/hr

Explanation
Let the present age of the baby be x. After 20 years, the baby's age will be x + 20. According to the problem, the baby's age after 20 years will be 5 times the present age , so we can set up the equation: x + 20 = 5x Subtract x from both sides: 20 = 4x Divide both sides by 4: 5 = x So, the present age of the baby is 5 years.