Explanation

Distance is directly proportional to speed when time is constant (12 : 9 = 4 : 3).

Solving the ratio gives the original distance as 30 km, so the increased distance is 30 + 10 = 40 km.

Explanation

The constant –1.50 represents a fixed service charge deducted from the total euros received.

This fee is independent of the amount of US dollars exchanged.

Explanation

For collinear points, slope between any two pairs is equal:

Slope(1,2) & (4,m) = Slope(4,m) & (5,6)

(m-2)/(4-1) = (6-m)/(5-4)

(m-2)/3 = 6-m

m-2 = 18-3m

4m = 20

m = 5

Explanation

Let's assume the interest rate is 12% p.a. (common in Pakistan):

Interest = Principal × Rate × Time

54,000 = P × 0.12 × 3

P = 54,000 / (0.12 × 3)

= 54,000 / 0.36

= 150,000

Explanation

Work done by 40 men in 40 days = 1/3 of total work

Total work = 3 × (40 × 40) = 4800 man-days

Remaining work = 2/3 of total work = 3200 man-days

Time left = 50 days

Men required = 3200 ÷ 50 = 64 men

Additional men needed = 64 − 40 = 24 men

Therefore, 24 more men are required.

Explanation

Let's solve the equation:

4^(2n+3) = 8^(n+5)

Expressing both sides with base 2:

(2^2)^(2n+3) = (2^3)^(n+5)

2^(4n+6) = 2^(3n+15)

Equating exponents:

4n + 6 = 3n + 15

4n - 3n = 15 - 6

n = 9

Explanation

Total food = 900 men × 30 days = 27,000 man-days

Men left = 900 - 150 = 750

Food will last = 27,000 man-days / 750 men = 36 days

Explanation

20% of 80,000 = 0.20 × 80,000 = 16,000

80,000 + 16,000 = 96,000

Explanation

Let the numbers be x, 2x, 3x.

Product = x × 2x × 3x = 6x³ = 750

x³ = 750/6 = 125

x = ∛125 = 5

Numbers are 5, 10, 15.

Highest number = 3x = 15

Explanation

45 minutes is ¾ of 1 hour, so the ratio is ¾.

Similarly, ¾ of 30 seconds = 22.5 seconds.