Govt Exams
Work = 5 × 12 = 60 man-days. For 3 days: Men needed = 60/3 = 20 men.
Cost price = 400. Marked price = 400 × 1.40 = 560. Selling price = 560 × 0.90 = 504. Profit = 504 - 400 = 104. Profit % = (104/400) × 100 = 26%.
Powers of 3 mod 7: 3^1=3, 3^2=2, 3^3=6, 3^4=4, 3^5=5, 3^6=1. Pattern repeats every 6. 100 = 16×6 + 4, so 3^100 ≡ 3^4 ≡ 4 (mod 7). Actually 3^4 = 81, 81 mod 7 = 4. Let me verify: 3^6 ≡ 1, so 3^100 = 3^(96+4) = (3^6)^16 × 3^4 ≡ 1 × 81 ≡ 4 (mod 7). Wait, checking again: 3^2=9≡2, 3^3≡6, 3^4≡4, 3^5≡5, 3^6≡1. So answer is 4.
Let the number be 100. After 20% increase: 120. After 20% decrease of 120: 120 × 0.8 = 96. Net change = 96 - 100 = -4, which is 4% decrease.
Total distance = 120 + 80 = 200 km. Total time = 2 + 1.5 = 3.5 hours. Average speed = 200/3.5 = 57.14 km/h. Wait, let me recalculate: 200/3.5 = 65.71 km/h.