Question

refer the attachment.​

Answer 1

Answer :

Let the numbers be x and y.

We know that Dividend = Divisor × Quotient + Remainder

As per the statement, "If the sum of two numbers is divided by 15, the quotient is 2 and the

remainder is 10 , we get x+y=15×2+10=>x+y=40 --- (1)

Also, as the difference of the same numbers is divided by 3

then the quotient is 4 and the remainder is 2, we get x−y=3×4+2=>x−y=14 --- (2)

Adding

equations 1 and 2, we get 2x=54=>x=27

Substituting

x=27 in the equation (1), we get 27+y=40=>y=13

Thus the numbers are 27,13

Answer 2

$\boxed{\mathrm{Solution}}$

Let two numbers be x and y

We know,

Dividend = Divisor × Quotient + Remainder.

As per the first given condition,

$\mathrm{x + y = 15 \times 2 + 10}$

$\mathrm{\implies \: x + y = 30 + 10}$

$\mathrm{\therefore \: x + y = 40 \: \: \: \: \: \: \: ...(1)}$

As per the second condition,

$\mathrm{x - y = 3 \times 4 + 2}$

$\mathrm{\implies \: x - y = 12 + 2 }$

$\mathrm{\therefore \: x - y = 14 \: \: \: \: \: \: \: \: \: ...(2)}$

Adding (1) and (2), we get,

x + y = 40

+ x - y = 14

______________________

2x = 54

______________________

$\mathrm{\implies \: x = \frac{54}{2} }$

$\mathrm{\therefore x = 27}$

Substituting x = 27 in (1)

$\mathrm{27 + y = 40}$

$\mathrm{\implies \: y = 40 - 27}$

$\mathrm{\therefore \: y = 13}$

Hence, the two numbers are 27 and 13.