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First we find the factors of 10500 i.e. 2*2*3*5*5*5*7
So to make it a perfect cube we have to divide this number by 2*2*3*7 i.e. 84
HCF = 23; numbers = 23x and 23y.
LCM = 644.
LCM*HCF = 23x*23y
644*23 = 23x*23y
xy = 28
x and y are co-prime numbers.
Possible pairs = 28 and 1, 7 and 4.
Numbers = 23 and 644 and 92 and 161
Sum = 667 and 253
From options, sum = 253.
Marks of 15 test takers = 15*240 = 3600
Marks of 10 test takers = 10*200 = 2000
Marks of remaining 5 test takers = 3600 – 2000 = 1600
Average = 16005 = 320
Distance covered by cyclist = 25 km; Distance covered by car = 1.5*30= 45 km
Ratio of car to cyclist = 25:45 = 5:9
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