41. In a kilometre race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 metres, the time taken by A to run 1 kilometre is. A. 250 seconds B. 205 seconds C. 200 seconds D. 210 seconds Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B Solution: Let the time taken by A to cover 1 km = $$x$$ seconds Time taken by B and C = $$x$$ + 30 seconds and $$x$$ + 45 seconds $$\eqalign{ & \frac{x}{{x + 45}} = \frac{{41}}{{50}} \cr & 50x = 41x + 1845 \cr & x = 205{\text{ seconds}} \cr} $$
42. In a 400 metre race, A runs at a speed of 16 m/sec. If A gives B a start of 15 metres and still beats him by 10 sec, then what is the speed of B? A. 11 m/sec B. 10 m/sec C. 13 m/sec D. 9 m/sec Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A Solution: \[\begin{array}{*{20}{c}} {}&{\text{A}}&{\text{B}} \\ {{\text{Distance}} \to }&{400}&{385} \end{array}\] $$\eqalign{ & \frac{{400}}{{\text{A}}} = \frac{{385}}{{\text{B}}} - 10 \cr & \frac{{400}}{{16}} = \frac{{385}}{{\text{B}}} - 10 \cr & 25 + 10 = \frac{{385}}{{\text{B}}} \cr & {\text{B}} = 11 \cr & {\text{Speed of B}} = 11{\text{ m/s}} \cr} $$
43. In a race of 1200 m, Ram can beat Shyam by 200 m or by 20 sec. What must be the speed of Ram? A. 14 m/sec B. 12 m/sec C. 10 m/sec D. 16 m/sec Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B Solution: Shyam's speed = $$\frac{{200}}{{20}}$$ = 100 m/sec. Time constant \[\begin{array}{*{20}{c}} {}&{{\text{Ram}}}&{}&{{\text{Shyam}}} \\ {{\text{Distance}} \to }&{1200}&:&{1000} \\ {}&{12}&:&{10} \\ {{\text{Speed}} \to }&{12}&:&{10 = 12} \end{array}\]
44. A can give 40 metres start to B and 70 metres to C in a race of one kilometre how many metres start can B give to C in a race of one kilometre? A. 30 metre B. $$\frac{{700}}{{29}}$$ metre C. $$31\frac{1}{4}$$ metre D. 32 metre Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option C Solution: \[\begin{array}{*{20}{c}} {\text{A}}&{\text{B}}&{\text{C}} \\ {1000}&{960}&{930} \end{array}\] ⇒ B can give C a start of 30 meters in a 960 meters race $$\eqalign{ & \Rightarrow 960\,{\text{units}} \to 30 \cr & 1\,{\text{unit}} \to \frac{1}{{32}} \cr & 1000\,{\text{units}} \to \frac{{1000}}{{32}} = 31\frac{1}{4}{\text{ meters}} \cr} $$
45. In a 1500 m race, Anil beats Bakul by 150 m and in the same race Bakul beats Charles by 75 m. By what distance does Anil beat Charles? A. 217.50 m B. 200.15 m C. 293.50 m D. 313.75 m Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A Solution: \[\begin{array}{*{20}{c}} {}&{{\text{Anil}}}&{}&{{\text{Bakul}}} \\ {{\text{Distance}} \to }&{1500}&{}&{1350} \\ {}&{10}&:&9 \\ {}&{{\text{Bakul}}}&{}&{{\text{Charles}}} \\ {{\text{Distance}} \to }&{1500}&{}&{1425} \\ {}&{60}&:&{57} \end{array}\] Anil beats Charles by $$\eqalign{ & = \frac{{87}}{{600}} \times 1500 \cr & = \frac{{435}}{2} \cr & = 217.50{\text{ m}} \cr} $$