Question

A two digit number is four times the sum and three times the product of it's digits . Find the number
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Answer 1

Answer:

Step-by-step explanation:let the digits be X and y

When we expand the number of will be 10x+y

The number 10x+y = 4(x+y)

10x+y=4x+4y

10x-4x=4y-y

6x=3y

2x=y ( first equation)

Next, 10x+y= 3(X*y)

10x+y=3xy

10x+2x= 3x * 2x ( substitute first equation y= 2x)

12x=6x2

By cancellation X= 2

y= 2x

y = 2*2

y = 4

The number is 10x+y

That is 10*2+4= 20+4=24

Answer 2

☯ Let the digits at tens and units place of the number be x and y respectively. Then,

Number = 10x + y

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Given that,

★ Number = 4 × Sum of the digits.

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

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

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

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

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

$:\implies{\boxed{\sf{\purple{y = 2x}}}}\;\bigstar$

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Also,

★ Number = 3 × Product of the digits.

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

$:\implies\sf 10x + 2x = 3 \times x \times 2x\qquad\qquad\bigg\lgroup\sf On\; eliminating\;y\bigg\rgroup$

$:\implies\sf 12x = 3 \times 2x^2$

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

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

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

$:\implies\bf x = 0\;or\;x = 2$

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⠀⠀⠀⠀⠀⠀☯ Since the given numbers is a two-digit number. So, its tens digit can't be zero.

Therefore,

• x = 2

• y = 2x = 2 × 2 = 4

☯ Hence, the required number is,

$:\implies\sf 10x + y$

$:\implies\sf 10 \times 2 + 4$

$:\implies{\boxed{\frak{\pink{24}}}}\;\bigstar$

$\therefore$ The required number is 24.