Races And Games - Study Mode

[#1] 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.
Correct Answer

(B) 205 seconds

Explanation

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 $$eqalign{
& frac{x}{{x + 45}} = frac{{41}}{{50}} cr
& 50x = 41x + 1845 cr
& x = 205{ ext{ seconds}} cr} $$

[#2] 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?
Correct Answer

(A) 11 m/sec

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{ ext{A}}&{ ext{B}} \
{{ ext{Distance}} o }&{400}&{385}
end{array}] $$eqalign{
& frac{{400}}{{ ext{A}}} = frac{{385}}{{ ext{B}}} - 10 cr
& frac{{400}}{{16}} = frac{{385}}{{ ext{B}}} - 10 cr
& 25 + 10 = frac{{385}}{{ ext{B}}} cr
& { ext{B}} = 11 cr
& { ext{Speed of B}} = 11{ ext{ m/s}} cr} $$

[#3] In a race of 1200 m, Ram can beat Shyam by 200 m or by 20 sec. What must be the speed of Ram?
Correct Answer

(B) 12 m/sec

Explanation

Solution: Shyam's speed = $$frac{{200}}{{20}}$$ = 100 m/sec. Time constant [x08egin{array}{*{20}{c}}
{}&{{ ext{Ram}}}&{}&{{ ext{Shyam}}} \
{{ ext{Distance}} o }&{1200}&:&{1000} \
{}&{12}&:&{10} \
{{ ext{Speed}} o }&{12}&:&{10 = 12}
end{array}]

[#4] 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?
Correct Answer

(C) $$31frac{1}{4}$$ metre

Explanation

Solution: [x08egin{array}{*{20}{c}}
{ ext{A}}&{ ext{B}}&{ ext{C}} \
{1000}&{960}&{930}
end{array}] ⇒ B can give C a start of 30 meters in a 960 meters race $$eqalign{
& Rightarrow 960,{ ext{units}} o 30 cr
& 1,{ ext{unit}} o frac{1}{{32}} cr
& 1000,{ ext{units}} o frac{{1000}}{{32}} = 31frac{1}{4}{ ext{ meters}} cr} $$

[#5] 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?
Correct Answer

(A) 217.50 m

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{{ ext{Anil}}}&{}&{{ ext{Bakul}}} \
{{ ext{Distance}} o }&{1500}&{}&{1350} \
{}&{10}&:&9 \
{}&{{ ext{Bakul}}}&{}&{{ ext{Charles}}} \
{{ ext{Distance}} o }&{1500}&{}&{1425} \
{}&{60}&:&{57}
end{array}] Anil beats Charles by $$eqalign{
& = frac{{87}}{{600}} imes 1500 cr
& = frac{{435}}{2} cr
& = 217.50{ ext{ m}} cr} $$