Entrance Exams
Govt. Exams
Number = 120/0.30 = 400. 25% of 400 = 100
Downstream speed = 15 km/h, Upstream speed = 10 km/h. Current = (15-10)/2 = 2.5 km/h
Combined rate = 1/10 + 1/15 = 5/30 = 1/6. Time = 6 hours
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
SP = MP × (100-discount%)/100 = CP × 1.4 × 0.8 = 1.12CP. Profit% = 12%
Using exponent rules: (2⁵ × 3⁴)/(2³ × 3²) = 2^(5-3) × 3^(4-2) = 2² × 3² = 4 × 9 = 36.
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.
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 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.
Let the number be x. According to problem: (5x)/12 = 20. Solving: 5x = 240, thus x = 48