The combined speed of 'Amit' and 'Bhanu' is ________ km/hr. 'Amit' traveled for 5 hours, and 'Bhanu' traveled for ______ hours in such a way that the distance covered by 'Bhanu' is 20 km less than that covered by 'Amit'. The speed of 'Amit' does not exceed 25 km/hr.

Which set of values from the following options will correctly fill the blanks in the given order to make the statement true:

I. 32, 2

II. 45, 3.2

III. 40, 10

Solution

ATQ, For I: Let speed of ‘Amit’ be ‘a’ km/hr Therefore, speed of ‘Bhanu’ = (32 – a) km/hr According to the question, 5a – 2(32 – a) = 20 Or, 5a + 2a – 64 = 20 Or, 7a = 84 Or, a = 12 Therefore, speed of ‘Amit’ = a = 12 km/hr Therefore, I is true. For II: Let speed of ‘Amit’ be ‘b’ km/hr Therefore, speed of ‘Bhanu’ = (45 – b) km/hr According to the question, 5b – 3.2(45 – b) = 20 Or, 5b + 3.2b – 144 = 20 Or, 8.2b = 164 Or, b = 20 Therefore, speed of ‘Amit’ = b = 20 km/hr Therefore, II is true. For III: Let speed of ‘Amit’ be ‘w’ km/hr Therefore, speed of ‘Bhanu’ = (40 – w) km/hr According to the question, 5w – 10(40 – w) = 20 Or, 5w + 10w – 400 = 20 Or, 15w = 420 Or, w = 28 Therefore, speed of ‘Amit’ = w = 28 km/hr Therefore, III is false.