A person covers a certain distance in 162 minutes, he covers 1/6 part of the distance at 25 km / h, ¾ part at 30 km / h and the remaining part at a speed of 40 km / h. What distance did the person travel?
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60
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70
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80
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90
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None of these
C
Correct answer
Explanation
Let total distance be D. Time taken for 1/6 of D at 25 km/h: (D/6)/25 = D/150 hours. Time for 3/4 of D at 30 km/h: (3D/4)/30 = D/40 hours. Time for remaining (1 - 1/6 - 3/4) = 1/12 of D at 40 km/h: (D/12)/40 = D/480 hours. Total time = D/150 + D/40 + D/480 = D × (16/2400 + 60/2400 + 5/2400) = D × 81/2400 hours. Given total time = 162 minutes = 2.7 hours. So D × 81/2400 = 2.7, therefore D = 2.7 × 2400/81 = 6480/81 = 80 km.