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.

Explanation

Let Zahra’s age = x, Ayesha’s age = y. Then 𝑥 × 𝑦 = 195

x×y=195. Factor pairs of 195: (1,195), (3,65), (5,39), (13,15).

Since Zahra is younger, Zahra = 13, Ayesha = 15.

Explanation

The sum of squares of first n natural numbers is given by:

1^2 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6

Explanation

80 percent of 700 is 560.

80 percent *700

= (80/100)*700

= (80*700)/100

= 56000/100 = 560