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1. 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

Discuss

Solution:

\begin{aligned} A : B = 100 : 90 \\ A : C = 100 : 72 \\ B : C = \frac{B}{A} \times \frac{A}{C} = \frac{90}{100} \times \frac{100}{72} = \frac{90}{72} \end{aligned}

When B runs 90 m, C runs 72 m.
When B runs 100m, C run

(\frac{72}{90} \times 100) m = 80 m

∴ B can give C 20 m

2. 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

Discuss

Solution:

\begin{aligned} A's speed = (5 \times \frac{5}{18}) m/sec \\ = \frac{25}{18} m/sec \\ Time taken by A to cover 100 m \\ = (100 \times \frac{18}{25}) \sec \\ = 72 \sec \\ ∴ Time taken by B to cover 92 m \\ = (72 + 8) = 80 \sec \\ ∴ B's speed = (\frac{92}{80} \times \frac{18}{5}) kmph \\ = 4.14 kmph \end{aligned}

3. 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

Discuss

Solution:

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

(\frac{4}{3} \times 360)

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.

4. 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 m

B. 4.5 m

C. 5 m

D. 6 m

Discuss

Solution:

\begin{aligned} A : B = 100 : 90 \\ A : C = 100 : 87 \\ \frac{B}{C} = \frac{B}{A} \times \frac{A}{C} \\ = \frac{90}{100} \times \frac{100}{87} \\ = \frac{30}{29} \end{aligned}

When B runs180m, C runs

(\frac{29}{30} \times 180) m = 174 m

∴ B beats C by (180 - 174) m = 6 m

5. 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 points

B. 20 points

C. 10 points

D. 12 points

Discuss

Solution:

\begin{aligned} A : B = 60 : 45 \\ A : C = 60 : 40 \\ ∴ \frac{B}{C} = \frac{B}{A} \times \frac{A}{C} = \frac{45}{60} \times \frac{60}{40} \\ = \frac{45}{40} = \frac{90}{80} = 90 : 80 \\ ∴ B can give C 10 points in a game of 90 \end{aligned}

6. 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

Discuss

Solution:

\begin{aligned} A : B = 200 : 169 \\ A : C = 200 : 182 \\ \frac{C}{B} = \frac{C}{A} \times \frac{A}{B} \\ = \frac{182}{200} \times \frac{200}{169} \\ = 182 : 169 \end{aligned}

When C covers 182 m, B covers 169 m
When C covers 350 m, B covers

(\frac{169}{182} \times 350) m = 325 m

∴ C beats B by (350 - 325) m = 25 m

7. 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

Discuss

Solution:

\begin{aligned} Distance covered by B in 9 sec \\ = (\frac{100}{45} \times 9) m \\ = 20 m \\ ∴ A beats B by 20 metres \end{aligned}

8. 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

Discuss

Solution:

\begin{aligned} A : B = 100 : 80 \\ A : C = 100 : 72 \\ ∴ \frac{B}{C} = \frac{B}{A} \times \frac{A}{C} = \frac{80}{100} \times \frac{100}{72} \\ = \frac{10}{9} = \frac{100}{90} = 100 : 90 \\ ∴ B can give C 10 points \end{aligned}

9. 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

Discuss

Solution:

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

10. 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

Discuss

Solution:

\begin{aligned} When B runs 25m, A runs \frac{45}{2} m \\ When B runs 1000m, A runs \\ = (\frac{45}{2} \times \frac{1}{25} \times 1000) m \\ = 900 m \\ ∴ B beats A by 100 m \end{aligned}

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