Question

if the sum two numbers is divided by 13, the quotient is 4 and the reminder is 8. if the difference of the same two numbers is divided by 4, the quotient is 3 and the remainder 2 . find the numbers​

Answer 1

ANSWER :-

Let the two numbers be x and y

We know,

Dividend = Divisor × Quotient + Remainder

As per the first condition,

x + y = 13 × 4 + 8

x + y = 52 + 8

x + y = 60 ............ ( i )

As per the second condition,

x - y = 4 × 3 + 2

x - y = 12 + 2

x - y = 14 ............. ( ii )

Adding eq ( i ) and ( ii ),

x + y = 60

x - y = 14

_____________________________

2x = 74

x = 37

Substituting x = 37 in eq ( i ),

37 + y = 60

y = 60 - 37

y = 23

Therefore, the two numbers are 37 and 23 .