Check each option: 125 = 5³ (perfect cube) ✓, 100 = 10² (not a perfect cube), 144 = 12² (not a perfect cube), 200 = 8 × 25 (not a perfect cube). Answer is 125.

Prime factorization: 48 = 2⁴ × 3, 64 = 2⁶, 80 = 2⁴ × 5. HCF is the product of lowest powers of common prime factors. Only 2 is common to all. Lowest power of 2 is 2⁴ = 16. Therefore, HCF = 16.

Check sum of digits: 121: 1+2+1 = 4 (not divisible by 3), 122: 1+2+2 = 5 (not divisible by 3), 123: 1+2+3 = 6 (divisible by 3) ✓, 124: 1+2+4 = 7 (not divisible by 3). Therefore 123 is divisible by 3.

Using exponent rules: (2⁵ × 3⁴)/(2³ × 3²) = 2^(5-3) × 3^(4-2) = 2² × 3² = 4 × 9 = 36.

SP = MP × (100-discount%)/100 = CP × 1.4 × 0.8 = 1.12CP. Profit% = 12%

Original speed = 120/8 = 15 km/h. New speed = 15 × 1.25 = 18.75 km/h. Distance in 5 hours = 18.75 × 5 = 93.75 km

When two pipes work together, their rates of filling add up. We use the concept of work rates: if a pipe fills a tank in \(t\) hours, its rate is \(\frac{1}{t}\) tanks per hour.

Step 1: Find the filling rate of each pipe

Pipe A fills the tank in 10 hours, so its rate is \(\frac{1}{10}\) tanks/hour.

Pipe B fills the tank in 15 hours, so its rate is \(\frac{1}{15}\) tanks/hour.

Step 2: Find the combined filling rate

When both pipes work together, their rates add:

Find a common denominator (LCM of 10 and 15 is 30):

Step 3: Calculate time to fill one complete tank

If the combined rate is \(\frac{1}{6}\) tanks per hour, then the time to fill 1 complete tank is:

Answer: Both pipes together will fill the tank in \(6\) hours (Option B)

Downstream speed = 15 km/h, Upstream speed = 10 km/h. Current = (15-10)/2 = 2.5 km/h

Number = 120/0.30 = 400. 25% of 400 = 100

Speed = Distance/Time = 150/12 = 12.5 m/s = 12.5 × 3.6 = 45 km/h