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Let CP = x; At 20% profit: SP = 1.2x; At 30% profit: SP = 1.3x; 1.3x - 1.2x = 60; 0.1x = 60; x = 600

After 15% discount: 85%; After 10% on that: 85×90/100 = 76.5%; Single discount = 100-76.5 = 23.5%

For three numbers: HCF(a,b,c)=12; LCM(a,b,c)=1440; HCF(60,84)=12; LCM(60,84)=420; Using extended property, third number = (HCF×LCM)/(HCF(a,b)×LCM(a,b)) approach: 60=12×5, 84=12×7, need 12×k where LCM(5,7,k)=120; k=12; so number=144

Relative speed = 60 + 40 = 100 km/h = 100×5/18 = 250/9 m/s; Total distance = 150+100 = 250m; Time = 250/(250/9) = 9 seconds

Downstream speed = 36/3 = 12 km/h; Current speed = 12 - 15 is wrong. Downstream = 15+c = 12 gives c = -3 (recalc: 36/3=12, so 15+c=12 is wrong); Let me recalc: Given makes no sense. If downstream is faster, 36/3=12 but boat is 15 km/h. Assume 60 km: 60/3=20; 20=15+c; c=5. For given: 15+c must be >15. Recheck: Actually c=3 means downstream 18 km/h, time=2 hours. Let assume answer verification: if c=3, downstream=18, time=36/18=2 hours (not 3). Error in question setup but answer given is C

6050 = 5000(1+r/100)²; 1.21 = (1+r/100)²; 1+r/100 = 1.1; r = 10%

Net rate = 1/10 + 1/15 - 1/20 = 6/60 + 4/60 - 3/60 = 7/60; Time = 60/7 ≈ 8.57 hours

Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36; Time = 36/5 = 7.2 days

48 = 2⁴×3; 64 = 2⁶; 96 = 2⁵×3; LCM = 2⁶×3 = 64×6 = 384

SP = 20 × 1.25 = ₹25; After 10% discount = 25 × 0.9 = ₹22.5; Profit% = (22.5-20)/20 × 100 = 12.5%