A car covers 1/6 of the distance from A to B at the speed of 12 km/hr, 1/9 of the distance at 36 km/hr and the remaining at the speed of 24 km/hr. Find the average speed of whole journey. एक कार A से B तक की दूरी का 1/6 भाग 12 किमी./घ. की गति से चलती है, 1/9 भाग 36 किमी/घ. की गति से चलती है और शेष 24 किमी/घं. की गति से चलती है। पूरी यात्रा की औसत गति ज्ञात कीजिए।
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24 km/hr./(किमी/घ.)
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29 km/hr./(किमी/घ.)
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21.24 km/hr./(किमी/घ.)
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26.8 km/hr./(किमी/घ.)
C
Correct answer
Explanation
Let total distance = D. Time for each part: t1 = (D/6)/12 = D/72, t2 = (D/9)/36 = D/324, t3 = (D - D/6 - D/9)/24 = (D × 11/18)/24 = 11D/432. Total time = D/72 + D/324 + 11D/432 = D(6/432 + 1.33/432 + 11/432) = D(18.33/432). Average speed = D / (18.33D/432) = 432/18.33 ≈ 23.56 km/hr. Hmm, this doesn't match. Let me recalculate: remaining = 1 - 1/6 - 1/9 = 13/18. Times: D/(6×12) = D/72, D/(9×36) = D/324, (13D/18)/24 = 13D/432. Total time = D(1/72 + 1/324 + 13/432) = D(6/432 + 1.33/432 + 13/432) = D(20.33/432). Speed = 432/20.33 ≈ 21.25 km/hr. This matches option C.