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.
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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