Question

the result of dividing a number of two digit by the number with the digit reversed is 7 by 4 if the sum the digit is 12 find the number

Answer 1

According to question,
$\binom{84}{72} = \binom{7}{2} \\ and \: 8 + 4 = 12 \: {proved}$
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Answer 2

Answer:

84

Step-by-step explanation:

Let the digit at 10s place be x and at ones place be y.

Then, original no. = 10x + y

And, reversed no. = 10y + x

Also, it is given that x + y = 12 - eqn.1

According to the question,

$\dfrac{10x + y}{10y + x} = \dfrac{7}{4}\\\\\\\implies 4(10x+y) = 7(10y+x)\\\\\\\implies 40x + 4y = 70y + 7x\\\\\\\implies 40x - 7x = 70y - 4y\\\\\\\implies 33x = 66y\\\\\\\implies x = 66y \div 33 = 2y\\\\\\\implies \bold{x = 2y} -- \text{eqn.2}$

From eqn.1 and eqn.2,

2y + y = 12

⇒ 3y = 12

⇒ y = 12 ÷ 3 = 4

⇒ y = 4

Put the value of y in eqn.1, we get

x + 4 = 12

⇒ x = 12 - 4 = 8

⇒ x = 8

Therefore, the required no. is 10x + y = 10(8) + 4 = 80 + 4 = 84.