Question

The ratio between a two digit number and
the numbes obtained'on Reversing its digit
is 4:7 . If the difference between the digits
of the number is 3 find the muniber.
3

Answer 1

Answer:

$\qquad\qquad\underline{\textsf{\textbf{ \color{magenta}{Solution\:completed} }}}$

Correct Question :-

• The ratio between a two digit number and
• the numbes obtained'on Reversing its digit
• is 4:7 . If the difference between the digits
• of the number is 3 find the number.

Solution :-

Let the ten's place digit be x

And the unit's place digit be y

Number = 10x + y

Reverse digit = 10y + x

So, according to the question or ATQ :-

➙ 10x + y / 10y + x = 4/7

➙ 7(10x + y) = 4(10y + x)

➙ 70x + 7y = 40y + 4x

➙ 70x - 4x + 7y - 40y = 0

➙ 66x - 33y = 0

➙ 33(2x - y) = 0

➙ 2x - y = 0 →(1)

➙ x - y = 3 →(2)

subtracting eqn (1) from (2)

➙ x - y - 2x + y = 3

➙ -x = 3

➙ x = -3

put x = -3 in eqn →(2)

➙ y = -3 - 3

➙ y = -6

Required Number = 10 x (3) + (6) = 36

Answer 2

Question

The ratio between a two digit number andthe numbes obtained'on Reversing its digitis 4:7 . If the difference between the digitsof the number is 3 find the number.

To find

two digit number

Answer

36

$\underline{ \boxed{\mathbb{\pink{Solution}}}} :- \\ </p><p></p><p>\tt{\implies}Let \: the \: ten's \: place \: digit \: be x \\ </p><p></p><p>\tt{\implies}And \: the \: unit's \: place \: digit \: be y \\ </p><p></p><p>\tt{\implies}{ \boxed{\mathbb{\red{number = 10x + y }}}}\\ </p><p></p><p>\tt{\implies}{ \boxed{\mathbb{\blue{Reverse digit = 10y + x}}}} \\ </p><p></p><p>So, \\  according  \: to \:  the \:  question  \: or ATQ :- \\ </p><p></p><p>➙ 10x + y / 10y + x = 4/7 \\ </p><p></p><p>➙ 7(10x + y) = 4(10y + x) \\ </p><p></p><p>➙ 70x + 7y = 40y + 4x \\ </p><p></p><p>➙ 70x - 4x + 7y - 40y = 0 \\ </p><p></p><p>➙ 66x - 33y = 0 \\ </p><p></p><p>➙ 33(2x - y) = 0 \\ </p><p></p><p>➙ 2x - y = 0 →(1) \\ </p><p></p><p>➙ x - y = 3 →(2) \\ </p><p></p><p>\tt{\implies}subtracting eqn (1) from (2) \\ </p><p></p><p>➙ x - y - 2x + y = 3 \\ </p><p></p><p>➙ -x = 3 \\ </p><p></p><p>➙ x = -3 \\ </p><p></p><p>\tt{\implies}put x = -3 in eqn →(2) \\ </p><p></p><p>➙ y = -3 - 3 \\ </p><p></p><p>➙ y = -6 \\ </p><p></p><p>\tt{\implies} \underline{ \boxed{\mathbb{\purple{Required Number = 10 \times (3) + (6) = 36}}}} \\ </p><p></p><p>$

Hope it helpful for you