Games and Race Problems LEVEL - 1
Q1–10 of 30In a 100 m race, A covers the whole distance in 36 seconds and B in 45 seconds. In this race, A beats B by
A covers 100 m in 36 s, B covers 100 m in 45 s. Distance A beats B by?
In 36 s, B covers $100 \times \dfrac{36}{45} = 80$ m
A beats B by $100 - 80 = 20$ m
Answer: (a) 20 m
In a kilometre race, A beats B by 100 m and B beats C by 150 m. In the same race, by how many metres does A beat C?
In a km race, A beats B by 100 m, B beats C by 150 m. Find by how much A beats C.
When B runs 1000 m, C runs 850 m
When B runs 900 m, C runs $850 \times \dfrac{900}{1000} = 765$ m
A beats C by $1000 - 765 = 235$ m
Answer: (b) 235 m
A can run 22.5 m while B runs 25 m. In a kilometre race, B beats A by
A runs 22.5 m while B runs 25 m. In a km race, find by how much B beats A.
Speed ratio $A:B = 22.5:25 = 9:10$
When B runs 1000 m, A runs $1000 \times \dfrac{9}{10} = 900$ m
B beats A by $1000 - 900 = 100$ m
Answer: (a) 100 m
In a kilometre race, A, B and C are three participants. A can give B a start of 50 m and C a start of 69 m. The start which B can allow C, is
In a km race, A gives B a start of 50 m and C a start of 69 m. Find the start B can give C.
When A runs 1000 m: B runs 950 m, C runs 931 m
When B runs 1000 m, C runs $931 \times \dfrac{1000}{950} = 980$ m
B can give C a start of $1000 - 980 = 20$ m
Answer: (d) 20 m
In a 1000 m race, A can beat B by 100 m. In a race of 400 m, B can beat C by 40 m. By how many metres will A beat C in a race of 500 m?
In a 1000 m race, A beats B by 100 m. In a 400 m race, B beats C by 40 m. Find by how much A beats C in a 500 m race.
$A:B = 1000:900 = 10:9$, $B:C = 400:360 = 10:9$
So $A:B:C = 10:9:8.1$
In a 500 m race, C covers $500 \times \dfrac{8.1}{10} = 405$ m
A beats C by $500 - 405 = 95$ m
Answer: (b) 95 m
In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by
In a 100 m race, A beats B by 10 m and C by 13 m. In a 180 m race, find by how much B beats C.
When B = 90, C = 87 (from the 100 m race data)
When B = 180, C = $87 \times \dfrac{180}{90} = 174$
B beats C by $180 - 174 = 6$ m
Answer: (d) 6 m
In a 200 m race, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:
In a 200 m race, A beats B by 31 m and C by 18 m. In a 350 m race, find by how much C beats B.
When A = 200: B = 169, C = 182
$\dfrac{C}{B} = \dfrac{182}{169} = \dfrac{13}{14}$
When C runs 350 m, B runs $350 \times \dfrac{13}{14} = 325$ m
C beats B by $350 - 325 = 25$ m
Answer: (b) 25 m
In a race of 200 m, B can give a start of 10 m to A and C can give a start of 20 m to B. The start that C can give to A in the same race is
In a 200 m race, B gives A a start of 10 m, and C gives B a start of 20 m. Find the start C can give A.
$\dfrac{A}{B} = \dfrac{190}{200} = \dfrac{19}{20}$, $\dfrac{C}{B} = \dfrac{200}{180} = \dfrac{10}{9}$
$\Rightarrow \dfrac{A}{C} = \dfrac{19}{20} \times \dfrac{9}{10} = \dfrac{171}{200}$
When C = 200, A = 171
C can give A a start of $200 - 171 = 29$ m
Answer: (b) 29 m
In a 200 m race, A beats B by 35 m or 7 seconds. A's time over the course is
In a 200 m race, A beats B by 35 m or 7 seconds. Find A's time.
B's speed $= \dfrac{35}{7} = 5$ m/s
When A finishes, B has run $200 - 35 = 165$ m
A's time $= \dfrac{165}{5} = 33$ sec
Answer: (c) 33 sec
In a 500 m race, the ratio of the speeds of two contestants A and B is $3:4$. If A has a start of 140 m, then A wins by
In a 500 m race, speed ratio $A:B = 3:4$. A has a start of 140 m. Find by how much A wins.
A runs $500 - 140 = 360$ m in time $\dfrac{360}{3k} = \dfrac{120}{k}$
B's distance in that time $= 4k \times \dfrac{120}{k} = 480$ m
A wins by $500 - 480 = 20$ m
Answer: (c) 20 m