Q28 of 29 Page 3

If five times the larger number of the two number is divided by smaller number, we get 5 as quotient and 3 as a remainder. Also, if seven times the smaller number is divided by the larger number, we get 5 as a quotient and 1 as a remainder. Find the numbers.

Let the larger number be x and smaller number be y.


As we know that,


Dividend = Divisor × quotient + remainder ….. (1)


When 5x is divided by y we get 5 as quotient and 3 as a remainder.


By (1)


5x = 5y + 3


5x – 5y – 3 = 0 ….. (2)


When 7y is divided by x we get 5 as a quotient and 3 as a remainder.


By (1)


7y = 5x + 1


5x – 7y – 1 = 0


By Method of cross multiplication:


a1x + b1y + c1 = 0


a2x + b2y + c2 = 0



Here a1= 5 a2 = 5


b1= –5 b2 = – 7


c1= –3 c2 = –1


So, for the given values,







x=1.6, y=1


Hence values of x and y are 1.6, 1.


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