Explanation

Total of 3 ages = 17 + 16 + 12 = 45

New average = 20, for 4 people → Total = 20 × 4 = 80

Age of 4th person = 80 − 45 = 35

Explanation

Mean = Total sum ÷ 3 → Total = 15 × 3 = 45

Given ages = 10 and 20 → Sum = 30

Third age = 45 − 30 = 15

Explanation

Ratio of boys to girls = 5:3

If 5 parts = 40 boys, then 1 part = 40 ÷ 5 = 8

Girls = 3 parts = 8 × 3 = 24 girls.

Explanation

Given x + 1/x = 5

To find x² + 1/x²:

(x + 1/x)² = x² + 2(x)(1/x) + 1/x²

= x² + 2 + 1/x²

x² + 1/x² = (x + 1/x)² - 2

= 5² - 2

= 25 - 2

= 23

Explanation

Given:

a : b : c = 2 : 5 (let's assume a common multiple for b and c to match both ratios)

b : c = 3 : 7

To match both ratios, let's find the LCM for b in both ratios.

Given a : b = 2 : 5 and b : c = 3 : 7, let's make the ratios comparable by finding a common multiple for b.

For a : b = 2 : 5 and b : c = 3 : 7,

let's scale a : b : c = 2_3 : 5_3 : 5*7 = 6 : 15 : 35

Now b : c = 15 : 35 which simplifies to 3 : 7.

Given a : b : c = 6 : 15 : 35

a : c = 6 : 35

Explanation

Multiply normally: 1 × 1 = 1

Count decimal places: 2 (from 0.01) + 3 (from 0.001) = 5

Place decimal: 0.00001

Explanation

Marked price = Rs 20,000

GST = 12% of 20,000

= 0.12 × 20,000

= Rs 2,400

Total amount = Marked price + GST

= 20,000 + 2,400

= Rs 22,400

Explanation

Population in 2020 = 50,000

Growth rate = 8%

Increase = 8% of 50,000

= 0.08 × 50,000

= 4,000

Population in 2021 = 50,000 + 4,000

= 54,000

Explanation

Original score = 72

Improvement = 15% of 72

= 0.15 × 72

= 10.8

New score = Original score + Improvement

= 72 + 10.8

= 82.8

Explanation

Original price = Rs 800

Discount = 25% of 800

= 0.25 × 800

= Rs 200

Final price = Original price - Discount

= 800 - 200

= Rs 600