Solve the following mathematical problems:

A two digit number is six times the sum of the two digits. If the digits are reversed, the number so obtained is 9 less than the original number. What is the original number?
(Number Concept)

dsuc.created: 2 years ago | dsuc.updated: 1 year ago

dsuc.updated: 1 year ago

Let, unit digit is y and tenth digit is x

$∴$ The number is (10x + y)

From 1st condition, 10x+y= 6(x + y).......(i)

And from 2nd condition, (10x + y) - (10y + x) = 9 ............... (ii)

Now, from equation (i)

10x + y = 6x + 6y

=4x = 5y

$∴$ x = $\frac{5 y}{4}$ …………………(iii)

Now, putting the value of x in equation (ii)

10x + y - (10y + x) = 9

= 10x + y - 10y - x = 9

=9x - 9y = 9

=(x - y) $\times$ 9 = 9

=x - y = 1

= $\frac{5 y}{4}$ - y = 1

= $\frac{5 y - 4 y}{4}$ = 1

$∴$ y = 4

Putting y = 4 in equation

(iii), we get

$∴$ x $\frac{5 \times 4}{4} = 5$

$∴$ The original number is 10x + y = (10 $\times$ 5) + 4 = 50 + 4 = 54 (answer)

1 year ago

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Rupali Bank Ltd. — Officer (22-11-2019) গণিত

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