Question

A two digit number is four times the sum and three times the product of its digits. Find the number.​

Answer 1

ANSWER:-

• The number is 24.

Answer 2

Answer:

Given :-

• A two digit number is four times the sum and three times the product of its digits.

To Find :-

• What is the number.

Solution :-

Let,

$\mapsto \bf Ten's\: Place =\: x$

$\mapsto \bf Unit's\: Place =\: y$

Then, the required number will be :

$\leadsto \bf Required\: Number =\: 10 \times x + y$

$\leadsto \sf\bold{\green{Required\: Number =\: 10x + y}}$

$\dag$ According to the question :

$\bigstar$ The two digits number is four times the sum of its digits.

So,

$\implies \bf 10x + y =\: 4 \times (Sum\: of\: Digits)$

$\implies \sf 10x + y =\: 4 \times (x + y)$

$\implies \sf 10x + y =\: 4(x + y)$

$\implies \sf 10x + y =\: 4x + 4y$

$\implies \sf 10x - 4x =\: 4y - y$

$\implies \sf 6x =\: 3y$

$\implies \sf \dfrac{6x}{3} =\: y$

$\implies \sf 2x =\: y$

$\implies \sf\bold{\purple{y =\: 2x\: ------\: (Equation\: No\: 1)}}$

Again,

$\bigstar$ The two digit number is three times the product of its digits.

So,

$\implies \bf 10 x + y =\: 3 \times (Product\: of\: Digits)$

$\implies \sf 10x + y =\: 3 \times (xy)$

$\implies \sf 10x + y =\: 3xy$

$\implies \sf 10x + 2x =\: 3x \times 2x$

$\implies \sf 12x =\: 6x^2$

$\implies \sf 6x^2 - 12x =\: 0$

$\implies \sf 6x(x - 2) =\: 0$

$\implies \bf 6x =\: 0$

$\implies \sf\bold{\blue{x =\: 0}}$

Or,

$\implies \sf x - 2 =\: 0$

$\implies \sf\bold{\blue{x =\: 2}}$

Hence, the value of x is 2.

Now, by putting x = 2 in the equation no 1 we get,

$\implies \bf y =\: 2x$

$\implies \sf y =\: 2 \times 2$

$\implies \sf\bold{\blue{y =\: 4}}$

Hence,

$\dag$ Required Number :

$\dashrightarrow \sf Required\: Number =\: 10x + y$

$\dashrightarrow \sf Required\: Number =\: 10 \times 2 + 4$

$\dashrightarrow \sf Required\: Number =\: 20 + 4$

$\dashrightarrow \sf\bold{\red{Required\: Number =\: 24}}$

$\sf\bold{\pink{\underline{\therefore\: The\: required\: number\: is\: 24\: .}}}$