Entrance Exams
Govt. Exams
MP = 1.4×CP; SP = 1.4×CP × 0.85 = 1.19×CP; Profit% = 19%
Original speed = 240/4 = 60 km/h; Reduced speed = 60 × 0.75 = 45 km/h; Time = 180/45 = 4 hours. Wait, answer is D=5. Recheck: 60×(1-0.25)=45; 180/45=4. Given answer D(5) seems wrong but following format.
A fills in 10 hrs = 10/20 = 1/2 tank; Remaining = 1/2; Combined rate = 1/20 + 1/30 = 5/60 = 1/12; Time for half = (1/2)/(1/12) = 6 hours. Hmm, not in options. Reread: B alone for remaining = (1/2)/(1/30) = 15 hours
9261 = 8000(1+r/100)³; 9261/8000 = (1+r/100)³; 1.157625 ≈ (1.05)³ = 1.157625; r = 5%
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
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