A two digit number is obtained by either multiplying sum of the digits

1.	A two digit number is obtained by either multiplying sum of the digits by 8 and adding 1 orby multiplying the difference of the digits by 13 and adding 2. Find the number.
Answer» Sol:Let the two digit number be 10x + y. Two digit number is obtained by multiplying sum of the digits by 8 and adding 1⇒ 10x + y = 8(x + y) + 1⇒ 2x - 7y = 1 ---------------- (1) Two digit number is obtained bymultiplying the difference of the digits by 13 and adding 2 ⇒10x + y = 13(x - y) + 2 ⇒3x - 14y = -2 ----------- (2) Solving equations 1 and 2, we get x = 4 and y = 1.Therefore, the two digit number is 41.

A two digit number is obtained by either multiplying sum of the digits by 8 and adding 1 orby multiplying the difference of the digits by 13 and adding 2. Find the number.

Answer»

Sol:Let the two digit number be 10x + y.

Two digit number is obtained by multiplying sum of the digits by 8 and adding 1⇒ 10x + y = 8(x + y) + 1⇒ 2x - 7y = 1 ---------------- (1)

Two digit number is obtained bymultiplying the difference of the digits by 13 and adding 2

⇒10x + y = 13(x - y) + 2

⇒3x - 14y = -2 ----------- (2)

Solving equations 1 and 2, we get x = 4 and y = 1.Therefore, the two digit number is 41.