25. Two men A and B walk from P to Q, a distance of 21 km at 3 km/h and 4 km/h respectively. B reaches at point Q and returns immediately and he meets A at point R. Find the distance from P to R.
a. 15 km
b. 18 km
c. 20 km
d. 24 km

Answer: B

Explanation:
Both of them together have walked twice the distance from P to Q i.e. 42 km.
Ratio of speeds of A and B = 3 : 4.
Therefore, Distance travelled by A = PR = $\displaystyle\frac{3}{7}$ x 42 = 18 km.

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26. Buses take 12 hr to cover the distance of 120 km between A and B. A bus starts from point A at 8.00 a.m. and another bus starts from point B at 10.00 a.m. on the same day. When do the two buses meet?
a. 2 pm
b. 3 pm
c. 4 pm
d. 5 pm

Answer: B

Explanation:
The distance between A and B is 120 km.
Speed of the buses = $\displaystyle\frac{{{\rm{120}}}}{{{\rm{12}}}}$ = 10 km/hr
By 10.00 a.m., the bus from A would have covered 20 km.
Hence, the distance between the buses at 10.00 a.m. = 120 – 20 = 100 km
Relative speed of the buses = 20 km/hr.
Time taken to meet = $\displaystyle\frac{{100}}{{20}}$ = 5 hr after B starts
i.e., the buses will meet at 3 p.m.

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27. Ravi started cycling along the boundaries of a square field from corner point A. After half an hour, he reached the corner point C, diagonally opposite to A. If his speed was 8 km/hr. what is the area of the field in square km ?
a. 64
b. 8
c. 4
d. Cannot be determined

Answer: A

Explanation:
As his speed is 8kmph, in half an hour he covers 4 kmph.
4 km is equal to two sides of the square.
So side of the square = 2 km
Area of the field = ${a^2}$ = 2 km x 2 km = 4 km

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28. A man walking at 3 km/hr crosses a square field diagonally in 2 min. The area of the field is :
a. 2500 ${m^2}$
b. 3000 ${m^2}$
c. 5000 ${m^2}$
d. 6000 ${m^2}$

Answer: C

Explanation:
Speed in meters per second = $\left( {3 \times \displaystyle\frac{5}{18}} \right)$ m/sec = $\left( {\displaystyle\frac{5}{6}} \right)$ m/sec.
Distance covered in $(2 \times 60)\sec .$ = $\left( {\displaystyle\frac{5}{6} \times 2 \times 60} \right)$m = 100 m
Length of diagonal = 100 m
So, area = $\displaystyle\frac{1}{2} \times $(diagonal)$^2$ = $\left( {\displaystyle\frac{1}{2} \times 100 \times 100} \right){m^2}$ = 5000${m^2}$

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29. A cart has to cover a distance of 80 km in 10 hours. If it covers half of the journey in (3/5)th time, what should be its speed to cover the remaining distance in the time left?
a. 8 km/hr
b. 20 km/hr
c. 6.4 km/hr
d. 10 km/hr.

Answer: D

Explanation:
Distance left = $\left( {\displaystyle\frac{1}{2} \times 80} \right)$ km = 40 km
Time left = $\left( {1 - \dfrac{3}{5}} \right) \times 10$ = $\displaystyle\frac{2}{5} \times 10 = 4$hrs
Speed required = (40$ \div $4) km/hr = 10 km/hr.

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30. The ratio between the rates of walking of P and Q is 2 : 3. If the time taken by Q to cover a certain distance is 36 minutes, the time taken by P to cover that much distance is :
a. 24 min
b. 54 min
c. 48 min
d. 21.6 min

Answer: B

Explanation:
We know that, ratio of times are inversely proportional to ratio of speeds.
Ratio of times taken = $\displaystyle\frac{1}{2}:\displaystyle\frac{1}{3}$ = 3 : 2
let the time taken by P is x minutes.
$\therefore$ 3 : 2 = x : 36
$ \Rightarrow \dfrac{3}{2} = \dfrac{x}{{36}}$
$\Rightarrow $ x = 54 min.