Explanation

Given:

a^2 + b^2 = 8 ... (Equation 1)

(a - b)^2 = 4

Expanding the left side of the equation: a^2 - 2ab + b^2 = 4

Now, substitute Equation 1 into this equation: 8 - 2ab = 4

Subtract 8 from both sides: -2ab = -4

Divide both sides by -2: ab = 2

So, the value of ab is 2.

Explanation

Let N of 1/12 = 3/48.

Then, N = 3/48 x 12 = 3/4

Explanation

Savings % = (100 – 65) % = 35 %

Saving = 35 % of Rs. 720

= Rs(35/100 ×720) = Rs. 252

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