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 $4^3 - frac{4^2}{2^2}$ 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.