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
Discussion
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
Discussion
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
Discussion
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
Discussion
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
Discussion
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%
Discussion
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
Discussion
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
Discussion
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
Discussion
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
Discussion
Explanation: Suppose A covers 400 m in t seconds
Then, B covers 385 m in (t + 5) seconds
$$\eqalign{ & {\text{ B covers 400 m in}} \cr & = \left\{ {\frac{{\left( {t + 5} \right)}}{{385}} \times 400} \right\}{\text{ sec}} \cr & = \frac{{80\left( {t + 5} \right)}}{{77}}{\text{ sec}} \cr & {\text{Also, B covers 400 m in}} \cr & = \left( {t + 7\frac{1}{7}} \right){\text{ sec}} \cr & = \frac{{\left( {7t + 50} \right)}}{7}{\text{ sec}} \cr & \frac{{80\left( {t + 5} \right)}}{{77}} = \frac{{7t + 50}}{7} \cr & 80\left( {t + 5} \right) = 11\left( {7t + 50} \right) \cr & \left( {80t - 77t} \right) = \left( {550 - 400} \right) \cr & 3t = 150 \cr & t = 50 \cr & {\text{ A's speed}} \cr & = \frac{{400}}{{50}}\,m/\sec \cr & = 8\,m/\sec \cr & {\text{B's speed}} \cr & = \frac{{385}}{{55}}\,m/\sec \cr & = 7\,m/\sec \cr} $$
11. In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:
a) 18 m
b) 20 m
c) 27 m
d) 9 m
Discussion
Explanation:
$$\eqalign{ & A:B = 100:90 \cr & A:C = 100:72 \cr & B:C = {B \over A} \times {A \over C} = {{90} \over {100}} \times {{100} \over {72}} = {{90} \over {72}} \cr} $$
When B runs 90 m, C runs 72 m.
When B runs 100m, C run
$$\left( {{{72} \over {90}} \times 100} \right)m = 80\,m$$
B can give C 20 m
12.A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
a) 5.15 kmph
b) 4.14 kmph
c) 4.25 kmph
d) 4.4 kmph
Discussion
Explanation:
$$\eqalign{ & {\text{A's}}{\kern 1pt} {\kern 1pt} {\text{speed}} = \left( {5 \times \frac{5}{{18}}} \right){\text{m/sec}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{25}}{{18}}{\text{m/sec}} \cr & {\text{Time}}{\kern 1pt} {\kern 1pt} {\text{taken}}{\kern 1pt} {\kern 1pt} {\text{by}}{\kern 1pt} {\kern 1pt} {\text{A}}{\kern 1pt} {\kern 1pt} {\text{to}}{\kern 1pt} {\kern 1pt} {\text{cover 100 m}} \cr & = \left( {100 \times \frac{{18}}{{25}}} \right)\sec \cr & = 72\sec \cr & {\text{Time}}{\kern 1pt} {\kern 1pt} {\text{taken}}{\kern 1pt} {\kern 1pt} {\text{by}}{\kern 1pt} {\kern 1pt} {\text{B}}{\kern 1pt} {\kern 1pt} {\text{to}}{\kern 1pt} {\kern 1pt} {\text{cover 92 m}} \cr & = \left( {72 + 8} \right) = 80\sec \cr & {\text{B's}}{\kern 1pt} {\kern 1pt} {\text{speed}} = \left( {\frac{{92}}{{80}} \times \frac{{18}}{5}} \right){\text{kmph}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4.14{\text{ kmph}} \cr} $$
13. In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
a) 60 m
b) 40 m
c) 20 m
d) 10 m
Discussion
Explanation: To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers $$\left( {\frac{4}{3} \times 360} \right)$$ m = 480 m.
Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
A wins by 20 m
14. 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:
a) 5.4
b) 4.5 m
c) 5 m
d) 6 m
Discussion
Explanation:
$$\eqalign{ & A:B = 100:90 \cr & A:C = 100:87 \cr & \frac{B}{C} = \frac{B}{A} \times \frac{A}{C} \cr & \,\,\,\,\,\,\,\, = \frac{{90}}{{100}} \times \frac{{100}}{{87}} \cr & \,\,\,\,\,\,\,\, = \frac{{30}}{{29}} \cr} $$
When B runs180m, C runs $$ \left( {\frac{{29}}{{30}} \times 180} \right){\text{m}} = 174{\text{m}}$$
B beats C by (180 - 174) m = 6 m
15. At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?
a) 30 point
b) 20 points
c) 10 points
d) 12 points
Discussion
Explanation:
$$\eqalign{ & A:B = 60:45 \cr & A:C = 60:40 \cr & \frac{B}{C} = {\frac{B}{A} \times \frac{A}{C}} = {\frac{{45}}{{60}} \times \frac{{60}}{{40}}} \cr & = \frac{{45}}{{40}} = \frac{{90}}{{80}} = 90:80 \cr & {\text{B}}\,{\text{can}}\,{\text{give}}\,{\text{C}}\,{\text{10}}\,{\text{points}}\,{\text{in}}\,{\text{a}}\,{\text{game}}\,{\text{of}}\,{\text{90}} \cr} $$
16. In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:
a) 86 sec
b) 80 sec
c) 76 sec
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{B runs}}\frac{{45}}{2}{\text{m in 6 sec}} \cr & {\text{B covers 300m in}} \cr & = \left( {6 \times \frac{2}{{45}} \times 300} \right)\sec \cr & = 80\,{\text{sec}} \cr} $$
17. A runs $$1\frac{2}{3}$$ times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
a) 200 m
b) 300 m
c) 270 m
d) 160 m
Discussion
Explanation: Ratio of speeds of A and B $$ = \frac{5}{3}:1 = 5:3$$
Thus, in race of 5m, A gains 2m over B
2m are gained by A in a race of 5m
80m will be gained by A in a race of
$$\left( {\frac{5}{2} \times 80} \right){\text{m}} = 200{\text{ m}}$$
Winning post is 200 m away from the starting point.
18.In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
a) 21 m
b) 26 m
c) 28 m
d) 29 m
Discussion
Explanation:
$$\eqalign{ & A:B = 100:75 \cr & B:C = 100:96 \cr & A:C = {\frac{A}{B} \times \frac{B}{C}} \cr & = {\frac{{100}}{{75}} \times \frac{{100}}{{96}}} \cr & = \frac{{100}}{{72}} \cr & 100:72 \cr & A\,\text{beats}\,C\,by \cr & = \left( {100 - 72} \right)m \cr & = 28\,m \cr} $$
19. 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 ?
a) 27 m
b) 29 m
c) 30 m
d) 25 m
Discussion
Explanation: B : A = 200 : 190
C : B = 200 : 180
$$\eqalign{ & = \frac{C}{A} \cr & = {\frac{C}{B} \times \frac{B}{A}} \cr & = {\frac{{200}}{{180}} \times \frac{{200}}{{190}}} \cr & = \frac{{200}}{{171}} \cr} $$
C can give to A, a start of (200 - 171) m = 29 m.
20. In a kilometre race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 m, the time taken by A to run 1 kilometre, is ?
a) 200 sec
b) 205 sec
c) 210 sec
d) 250 sec
Discussion
Explanation: In a km race, suppose A takes t sec,
Then, B takes (t + 30) sec, and C takes (t + 45) sec
180 m is covered by C in 45 sec
1000 m is covered by C in
= $$\left( {\frac{{45}}{{180}} \times 1000} \right)$$ sec
= 250 sec
A covers 1000 m in
= (250 - 45) sec
= 205 sec