Question

If the sum of two no. is divided by 15, the quotient is 2 and the remainder is 10. If the difference of the same numbers is divided by 3, then the quotient is 4 and the remainder is 2. find the numbers.

Answer 1

Step-by-step explanation:

the numbers are 27 and 13

$let \: the \: no. \: be \: x \: and \: y \\ we \: know \: dividend \: = divisor \times quotient + remainder \\ according \: to \: question \\ case \: 1 \\ dividend \: is \: (x + y) \\ divisor \: is \: 15 \\ quotient \: is \: 2 \: and \\ remainder \: is \: 10 \\ x + y = 15 \times 2 + 10 \\ x + y = 30 + 10 \\ x + y = 40 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ....... \: (1) \\ case \: 2 \ \\ dividend \: is \: (x - y) \\ divisor \: is \: 3 \\ quotient \: is \: 4\: and \\ remainder \: is \: 2\\ x - y = 3 \times 4 + 2 \\ x - y = 12 + 2\\ x - y = 14\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ....... \: (2) \\ \\ from \: (1) \: and \: (2) \\ x + y = 40 \\ x - y = 14 \\ 2x = 54 \: \: \: \: \: \: \: (elimination) \\ x = \frac{54}{2} \\ x = 27 \\ on \: putting \: value \: of \: x \: in \: (1) \\ x + y = 40 \\ 27 + y = 40 \\ y = 40 - 27 \\ y = 13$