Question

a two digit number is such that the product of its digit is 35 when 18 is added to the number the digits interchange their places find the number ​

Answer 1

Let ten's digit be M and one's digit be N.

A two digit number is such that the product of its digit is 35.

According to question,

=> MN = 35

=> M = 35/N _____ (eq 1)

When 18 is added to the number the digitw interchange their place.

Original number = 10M + N

Interchanged number = 10N + M

According to question,

=> 10N + M = 10M + N + 18

=> 10N - N + M - 10M = 18

=> 9N - 9M = 18

=> N - M = 2

=> N - 35/N = 2 [From (eq 1)]

=> (N² - 35)/N = 2

=> N² - 35 = 2N

=> N² - 2N - 35 = 0

=> N² - 7N + 5N - 35 = 0

=> N(N - 7) +5(N - 7) = 0

=> (N + 5) (N - 7) = 0

=> N = 7, -5 (Neglected)

Put value of N in (eq 1)

=> M = 35/7

=> M = 5

So,

Original number = 10M + N

=> 10(5) +7

=> 57

∴ Original number is 57.

Answer 2

Answer:

${\bold{\therefore Number=57}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about a number and the relation between its ones and tens place digit.

• We have to find the number.

$\underline \bold{Given : } \\ \bold{Let \: number \: in \: Ones \: place = x} \\ \bold{Tens \: place \: number = y} \\ \implies xy = 35 \\ \bold{Original \: number} \\ \implies 10x + y \\ \bold{Interchange \: number} \\ \implies 10x + y + 18 = 10y + x \\ \\ \underline \bold{To \: Find : } \\ \implies Number = ?$

• According to given question :

$\implies xy = 35 \\ \implies x = \frac{35}{y} - - - - - (1) \\ \\ \implies 10x + y + 18= 10y + x - - - - - (2) \\ \bold{Puting \: value \: of \: x \: in \: (2)}\\ \implies 10 \times \frac{35}{y} + y + 18 = 10y + \frac{35}{y} \\ \implies \frac{350 + {y}^{2} + 18y }{y} = \frac{10 {y}^{2} + 35}{y} \\ \implies 9 {y}^{2} - 18y - 315 = 0 \\ \implies {y}^{2} - 2y - 35 = 0 \\ \implies {y}^{2} - 7y + 5y - 35 = 0 \\ \implies y(y -7) + 5(y - 7) = 0 \\ \implies y = - 5 \: and \: 7 \\\bold{Negative\:number\:is\:neglected}\\ \bold{\implies y = 7} \\ \\ Puting \: value \: of \: y \: in \: (1) \\ \implies x = \frac{35}{y} \\ \implies x = \frac{35}{7} \\ \bold{\implies x = 5} \\ \\ \bold{\therefore Number = xy = 57}$