1. In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:
a) 22.75 m
b) 25 m
c) 19.5 m
d) $$7\frac{4}{7}$$ m
Explanation:
$$\eqalign{ & A:B = 200:169 \cr & A:C = 200:182 \cr & \frac{C}{B} = {\frac{C}{A} \times \frac{A}{B}} \cr & \,\,\,\,\,\,\,\, = {\frac{{182}}{{200}} \times \frac{{200}}{{169}}} \cr & \,\,\,\,\,\,\,\, = 182:169 \cr} $$
When C covers 182 m, B covers 169 m
When C covers 350 m, B covers $$\left( {\frac{{169}}{{182}} \times 350} \right){\text{m}} = 325{\text{m}}$$
C beats B by (350 - 325) m = 25 m
2. In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
a) 20 m
b) 25 m
c) 22.5 m
d) 9 m
Explanation:
$$\eqalign{ & {\text{Distance covered by B in 9 sec}} \cr & = \left( {\frac{{100}}{{45}} \times 9} \right){\text{m}} \cr & = 20\,{\text{m}} \cr & {\text{A beats B by 20 metres}} \cr} $$
3. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:
a) 8 points
b) 10 points
c) 14 points
d) 40 points
Explanation:
$$\eqalign{ & A:B = 100:80 \cr & A:C = 100:72 \cr & \frac{B}{C} = {\frac{B}{A} \times \frac{A}{C}} = {\frac{{80}}{{100}} \times \frac{{100}}{{72}}} \cr & = \frac{{10}}{9} = \frac{{100}}{{90}} = 100:90 \cr & {\text{B}}\,{\text{can}}\,{\text{give}}\,{\text{C}}\,{\text{10}}\,{\text{points}} \cr} $$
4. In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:
a) 40 sec
b) 47 sec
c) 33 sec
d) None of these
Explanation: B runs 35m in 7sec
B covers 200m in $$ {\frac{7}{{35}} \times 200} = 40\sec $$
B's time over the course = 40 sec
A's time over the course (40 - 7) sec = 33 sec
5. A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:
a) 100 m
b) $$111\frac{1}{9}$$ m
c) 25 m
d) 50 m
Explanation:
$$\eqalign{ & {\text{When}}\,{\text{B}}\,\,{\text{runs}}\,{\text{25m,}}\,{\text{A}}\,{\text{runs}}\,\frac{{45}}{2}m \cr & {\text{When}}\,{\text{B}}\,\,{\text{runs}}\,{\text{1000m,}}\,{\text{A}}\,{\text{runs}} \cr & = \left( {\frac{{45}}{2} \times \frac{1}{{25}} \times 1000} \right)m \cr & = 900 \,m \cr & {\text{B}}\,{\text{beats}}\,{\text{A}}\,{\text{by}}\,{\text{100 m}} \cr} $$
6. A team played 40 games in a season and won in 24 of them. What percent of games played did the team win ?
a) 70%
b) 40%
c) 60%
d) 35%
Explanation: Number of games played = 40
Number of won games = 24
Percentage of games played
= $$\left( {\frac{{24}}{{40}} \times 100} \right)$$
= 60%
7. In a kilometre race, A, B and C are three participants. A can give B start of 50 m and C a start of 69 m. The start which B can allow C, is -
a) 17 m
b) 18 m
c) 19 m
d) 20 m
Explanation: A : B : C
= 1000 : (1000 - 50) : (1000 - 69)
= 1000 : 950 : 931
In a 950 m race, B can give C a start of
(950 - 931) m
= 19 m
In a 1000 m race, B can give C a start of
= $$\left( {\frac{{19}}{{950}} \times 1000} \right)$$
= 20 m
8. A and B take part in a 100 metres race. A runs at 5 km an hour. A gives B a start of 8 metres and still beats him by 8 seconds. The speed of B is ?
a) 4.45 km/hr
b) 4.14 km/hr
c) 4.15 km/hr
d) 4.25 km/hr
Explanation: A's speed = 5 km/hr
= $$\left( {5 \times \frac{5}{{18}}} \right)$$ m/sec
= $$\frac{25}{18}$$ m/sec
Time taken by A to cover 100 metres
= $$\left( {100 \times \frac{{18}}{{25}}} \right)$$
= 72 sec
Time taken by B to cover 92 metres
= (72 + 8) sec
= 80 sec
B's speed
$$\frac{92}{80}$$ m/sec
= $$\left( {\frac{{92}}{{80}} \times \frac{{18}}{5}} \right)$$ km/hr
= $$\frac{414}{100}$$ km/hr
= 4.14 km/hr
9. Four sisters Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs. 32. How much money did Suvarna start with ?
a) Rs. 60
b) Rs. 34
c) Rs. 66
d) Rs. 28
Explanation:
| End of | Suvarna | Tara | Uma | Vibha |
| 4th Game | 32 | 32 | 32 | 32 |
| 3rd Game | 16 | 16 | 16 | 80 |
| 2nd Game | 8 | 8 | 72 | 40 |
| 1st Game | 4 | 68 | 36 | 20 |
| Original Money |
62 | 34 | 18 | 10 |
Survarna starts with Rs. 66
10. In a 400 m race, A gives B a start of 5 seconds and beats him by 15 m. In another race of 400 m, A beats B by $$7\frac{1}{7}$$ seconds. Their respective speed are
a) 6 m/sec, 7 m/sec
b) 5 m/sec, 7 m/sec
c) 8 m/sec, 7 m/sec
d) 9 m/sec, 7 m/sec
Explanation: Suppose A covers 400 m in t seconds
Then, B covers 385 m in (t + 5) seconds
$$\eqalign{ & {\text{ B covers 400 m in}} \cr & = \left\{ {\frac{{\left( {t + 5} \right)}}{{385}} \times 400} \right\}{\text{ sec}} \cr & = \frac{{80\left( {t + 5} \right)}}{{77}}{\text{ sec}} \cr & {\text{Also, B covers 400 m in}} \cr & = \left( {t + 7\frac{1}{7}} \right){\text{ sec}} \cr & = \frac{{\left( {7t + 50} \right)}}{7}{\text{ sec}} \cr & \frac{{80\left( {t + 5} \right)}}{{77}} = \frac{{7t + 50}}{7} \cr & 80\left( {t + 5} \right) = 11\left( {7t + 50} \right) \cr & \left( {80t - 77t} \right) = \left( {550 - 400} \right) \cr & 3t = 150 \cr & t = 50 \cr & {\text{ A's speed}} \cr & = \frac{{400}}{{50}}\,m/\sec \cr & = 8\,m/\sec \cr & {\text{B's speed}} \cr & = \frac{{385}}{{55}}\,m/\sec \cr & = 7\,m/\sec \cr} $$