Question
In a race of 300 metres, 'P' defeats 'R' by 45 metres, and
'R' defeats 'Q' by 30 metres. Find out how many metres 'P' defeats 'Q' by.Solution
ATQ,
Let the time taken by 'P' to finish = t seconds
Then, distance covered by 'R' in t seconds = 300 - 45 = 255 metres
So, ratio of speeds of 'P' and 'R' = 300 : 255 = 20 : 17
Now, R beats Q by 30 metres, so:
Ratio of speeds of 'R' and 'Q' = 300 : (300 - 30) = 300 : 270 = 10 : 9
Now, combine:
Ratio of speeds of P, R, Q = 20×10 : 17×10 : 17×9 = 200 : 170 : 153
So, when 'P' runs 300 metres, 'Q' runs = 300 × (153/200) = 229.5 metres
Therefore, 'P' beats 'Q' by 300 - 229.5 = 70.5 metres
205     255     292     ?     335     345
...14Â Â Â Â Â 15Â Â Â Â Â Â Â 32Â Â Â Â Â Â 99Â Â Â Â Â Â 400Â Â Â Â Â Â ?
...32, ?, 41, 68, 132, 257
...If  2  4  6  x  14  28  30
Then, x³+ 2 x+1 = ?
5Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9Â Â Â Â Â Â Â Â Â Â Â Â Â Â 30Â Â Â Â Â Â Â Â Â Â Â 115Â Â Â Â Â Â Â Â Â 582Â Â Â Â Â Â Â Â Â 3483
15Â Â Â Â ...
If   314     306      x      269       394    178    1480
Then, 1/3 x + 2x - x = ?
...29    51    95    183    ?     711
5     16     ?      66     119      200
...28         57           172           689          ?              20677
...21     84      168      172     ?     348
...
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