Q. 83.5( 13 Votes )

If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder.

Find the numbers.

Answer :

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


We know that -


Dividend = Quotient Divisor + Remainder


According to question -


3x = 4y + 8


3x - 4y = 8.....(1)


and, 5y = 3x + 5


- 3x + 5y = 5.....(2)


From equation (1), we get -


x = (4y + 8)/3.....(3)


Substituting the value of x in equation (2), we get -





y - 8 = 5


y = 13


substituting the value of y in equation (3), we get -


x = 20


Thus, the numbers are 20 and 13.


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