Question

A two digit number is 4 times the sum of its digits and 2 times the product of it's digits. Calculate the number.

Answer 1

Hi friend
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Your answer
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Let the digit at the ones place be y and the digit at the tens place be x.

Then, the number = 10x + y

Now,
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SOLVING (BY METHOD OF SUBSTITUTION)
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According to the question,
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Equations : -
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10x + y = 4(x + y) .....(i)

10x + y = 2xy......(ii)

From equation (i), we get,
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10x + y = 4(x + y)

=> 10x + y = 4x + 4y

=> 10x - 4x = 4y - 3y

=> 6x = 3y

=> x = 3y/6

=> x = y/2 ......(iii)

Now,
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Substituting the value of x from equation (iii) in equation (ii), we get,
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10x + y = 2xy

=> 10 × y/2 + y = 2 × y/2 × y

=> 5y + y = y²

=> 6y = y²

=> y = 6

Now,
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Putting the value of y in equation (ii),we get,
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x = y/2

=> x = 6/2

=> x = 3

Therefore,
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The number = 10x + y = (10 × 3) + 6 = 30 + 6 = 36