Question

The sum of the digits of a two digit number is 14 and the difference between the two digit of the number is 2. What is the product of the two digits of the two digit number

Answer 1

Answer:

let the tens digit of the required number be X and the units digit be Y

Step-by-step explanation:

Required no.=(10x + y)

Now, according to question

x + y=14 ------(1)

x - y =2 ------(2)

Adding eqn. no. (1) and (2),we get

2x =16

x = 8

putting the value of x in (1),we get

8 + y = 14

y = 14 - 8 = 6

Hence the required no. = x × y

= 8 × 6

= 48 Ans.

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• The sum of the digits of a two digit number is 14

$\:\:$

• Difference between the two digit of the number is 2

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• Product of the two digits of the two digit number

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the ones digit be 'a'

Let the tens digit be 'b'

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

$\underline{\bold{\texttt{Sum of digits is 14 </p><p>}}}$

$\:\:$

$\purple\longrightarrow$ $\sf a + b = 14$ -----(1)

$\:\:$

$\underline{\bold{\texttt{Difference of digits is 2</p><p>}}}$

$\:\:$

$\purple\longrightarrow$ $\sf a - b = 2$ -------(2a)

$\:\:$

Or,

$\:\:$

$\purple\longrightarrow$ $\sf b - a = 2$ ------(2b)

$\:\:$

$\underline{\bold{\texttt{Adding (1) \& (2a)}}}$

$\:\:$

$\sf \longmapsto a + b + a - b = 14 + 2$

$\:\:$

$\sf \longmapsto 2a = 16$

$\:\:$

$\sf \longmapsto a = \dfrac { 16 } { 2 }$

$\:\:$

$\bf \dashrightarrow a = 8$

$\:\:$

$\underline{\bold{\texttt{Putting a = 8 in (1)}}}$

$\:\:$

$\sf \longmapsto 8 + b = 14$

$\:\:$

$\sf \longmapsto b = 14 - 8$

$\:\:$

$\bf \dashrightarrow b = 6$

$\:\:$

$\underline{\bold{\texttt{Product of digits :}}}$

$\:\:$

$\bf \dag \: \: 6 \times 8$

$\:\:$

$\bf \dashrightarrow 48$

$\:\:$

$\underline{\bold{\texttt{Adding (1) \& (2b)}}}$

$\:\:$

$\sf \longmapsto a + b + b - a = 14 + 2$

$\:\:$

$\sf \longmapsto 2b = 16$

$\:\:$

$\sf \longmapsto b = \dfrac { 16 } { 2 }$

$\:\:$

$\bf \dashrightarrow b = 8$

$\:\:$

$\underline{\bold{\texttt{Putting b = 8 in (1)}}}$

$\:\:$

$\sf \longmapsto a + 8 = 14$

$\:\:$

$\sf \longmapsto a = 14 - 8$

$\:\:$

$\bf \dashrightarrow a = 6$

$\:\:$

$\underline{\bold{\texttt{Product of digits :}}}$

$\:\:$

$\bf \dag \: \: 8 \times 6$

$\:\:$

$\bf \dashrightarrow 48$

Hence product is 48 from both the cases.

$\rule{200}5$