Question

according to euclid's division lemma a=bq+, where b represents divisor and r represents remainder. if sum of all possible value of r is 120, then value of b is

A. 14
B. 15
C. 16
D. 20

Answer 1

Given : According to euclid division lemma a=bq+r where sum of all possible values of r is 120  

To Find : value of b

A. 14

B. 15

C. 16

D. 20

Solution:

According to euclid division lemma a=bq+r

0 ≤  r <  b

Hence value of r

are  0 , 1 , 2 , 3 , _________ , b - 1

Hence total possible values = b

Sum = (b/2)( 0 + b - 1)

= b(b - 1)/2  

b(b - 1)/2   = 120

=> b(b -1)  = 240

=> b² - b - 240 = 0

=> b² - 16b + 15b - 240 = 0

=> (b - 16)(b + 15) = 0

=> b = 16   as b can not be negative

Hence Value of b is 16

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