P and Q take part in a 400 m race. P runs at 12 km/hr. P gives Q a start of 20 m and still beats him by 13 seconds. The speed of Q is (round up to two decimal places).

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**Solution:**

1. Convert speed of P from km/hr to m/s:
   $$12 	imes \frac{5}{18} = \frac{10}{3} 	ext{ m/s}$$

2. Calculate time taken by P to complete 400 m:
   $$	ext{Time}_P = \frac{400}{10/3} = 400 	imes \frac{3}{10} = 120 	ext{ seconds}$$

3. Since P beats Q by 13 seconds, time taken by Q:
   $$	ext{Time}_Q = 120 + 13 = 133 	ext{ seconds}$$

4. Distance covered by Q (given a start of 20 m):
   $$400 - 20 = 380 	ext{ m}$$

5. Calculate speed of Q in m/s:
   $$	ext{Speed}_Q = \frac{380}{133} \approx 2.8571 	ext{ m/s}$$

6. Convert speed of Q to km/hr:
   $$2.8571 	imes \frac{18}{5} = 10.2857 \approx 10.29 	ext{ km/hr}$$

**Answer:** $10.29 	ext{ km/hr}$

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