Question

A two digit number is obtained either by multiplying the sum of the digits by 7 and adding 3 or multiplying the difference of digits by 17 and adding 1, The number is
a)54
b) 52
c ) 25
d) 30
​

Answer 1

$\huge\fbox\pink{a} \fbox\blue{n}\fbox \green{s} \fbox \red{w} \fbox\orange{e} \fbox\purple{r}$

$\sf\bold{given:}$

• two number are x and y
• number is become 10x+y

$\bf{condition \: 1:}$

• sum of two number [ x+y ] multiplied by 7 and added 3

...

$\sf{➲ 10x+y = 7[ x+y ]+3}$

$\sf{➲10x+y = 7x +7y +3}$

$\sf{➲3x-6y = 3}$

..

$\bf{condition \: 2:}$

• difference of two digit[ x-y ] multiple by 17 and plus 1

..

$\sf{➲10x+y = 17[ x-y ]+1}$

$\sf{➲10x+y = 17x-17y+1}$

$\sf{➲7x-18y = -1}$

$\large\bf{equation \:: }$

..

$\bf\boxed{ ➲\frac{9x-18y = 9}{7x-18y = -1}}$

$\sf{➲2x = 10}$

$\sf{➲x \: = 5}$

...

$\sf{➲9x-18y = 9}$

$\sf{➲9 \times 5-18y = 9}$

$\sf{➲45-18y = 9}$

$\sf{➲-18y = -36}$

$\sf{➲y = 2}$

$\large\bf\red{\boxed{answer= b . 52}}$

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