Explanation

First, calculate the total sum: average × 5

Then subtract the marks of the student who left, and divide the result by 4 to get the new average.

Explanation

Given:

Average = 18

Numbers: 7, 13, 17, x, 29

Average = (Sum of numbers) / (Total count)

18 = (7 + 13 + 17 + x + 29) / 5

Multiply both sides by 5:

90 = 66 + x

x = 90 - 66

x = 24

Explanation

Given:

xy = 35

x + y = 12

To find x² + y²:

(x + y)² = x² + 2xy + y²

144 = x² + 2(35) + y²

144 = x² + 70 + y²

x² + y² = 144 - 70

= 74

Explanation

Given:

3x : 2y = 6 : 5

Cross-multiply:

(3x) × 5 = (2y) × 6

15x = 12y

Divide both sides by 3y:

5x/y = 4

x/y = 4/5

So, x : y = 4 : 5

Explanation

Given:

Initial value = 80

Final value = 80

Percentage increase = ((Final - Initial) / Initial) × 100

= ((80 - 80) / 80) × 100

= (0 / 80) × 100

= 0%

Explanation

Given x + 1/x = 3

To find x³ + 1/x³:

(x + 1/x)³ = x³ + 3(x²)(1/x) + 3(x)(1/x)² + 1/x³

= x³ + 3x + 3/x + 1/x³

= x³ + 1/x³ + 3(x + 1/x)

(x + 1/x)³ = x³ + 1/x³ + 3(3)

27 = x³ + 1/x³ + 9

x³ + 1/x³ = 27 - 9

= 18

Explanation

Given equation:

3/x + 2/(x+1) = 1

Multiply both sides by x(x+1):

3(x+1) + 2x = x(x+1)

Expanding both sides:

3x + 3 + 2x = x² + x

Combine like terms:

5x + 3 = x² + x

Rearrange the equation:

x² - 4x - 3 = 0

Solve the quadratic equation:

x = (4 ± √(16 + 12)) / 2

x = (4 ± √28) / 2

x = (4 ± 2√7) / 2

x = 2 ± √7

The answer is 2 + √7 or 2 - √7.

Explanation

Let's denote A's rate of work as A, and B's rate of work as B.

Given A + B together complete the work in 12 days:

(A + B)'s 1 day's work = 1/12

B alone completes the work in 20 days:

B's 1 day's work = 1/20

A's 1 day's work = (A + B)'s 1 day's work - B's 1 day's work

= 1/12 - 1/20

= (5 - 3) / 60

= 2 / 60

= 1 / 30

A alone will complete the work in 30 days.

Explanation

Profit = 20% of Rs. 180 = 20/100 × 180 = 36

Selling Price = Cost Price + Profit = 180 + 36 = Rs. 216

Explanation

Let's denote the cost price as CP.

Given selling price (SP) = Rs 2400

Loss percentage = 20%

CP = SP / (1 - Loss percentage)

= 2400 / (1 - 0.20)

= 2400 / 0.80

= Rs 3000