Question

the denominator of a fraction is 12 more than the numerator if 16 is added to both the numerator and the denominator the fraction so obtained is 10 upon 13 find the all India section​

Answer 1

Answer: 24

Step-by-step explanation:

Answer 2

Correct Question:

The denominator of a fraction is 12 more than the numerator. If 16 is added to both the numerator and the denominator, the fraction so obtained is 10 / 13. Find the fraction.

Answer:

$\boxed{\red{\sf\:The\:required\:fraction\:=\:\frac{24}{36}}}$

Step-by-step-explanation:

Let the numerator of the fraction be x.

And the denominator of the fraction be y.

From the first condition,

y = x + 12 - - - ( 1 )

From second condition,

$\sf\:\dfrac{x\:+\:16}{y\:+\:16}\:=\:\dfrac{10}{13}\\\\\implies\sf\:13\:(\:x\:+\:16\:)\:=\:10\:(\:y\:+\:16\:)\\\\\implies\sf\:13x\:+\:208\:=\:10\:[\:(\:x\:+\:12\:)\:+\:16\:]\:\:\:-\:-\:[\:From\:(\:1\:)\:]\\\\\implies\sf\:13x\:+\:208\:=\:10\:[\:x\:+\:12\:+\:16\:]\\\\\implies\sf\:13x\:+\:208\:=\:10\:[\:x\:+\:28\:]\\\\\implies\sf\:13x\:+\:208\:=\:10x\:+\:280\\\\\implies\sf\:13x\:-\:10x\:=\:280\:-\:208\\\\\implies\sf\:3x\:=\:72\\\\\implies\sf\:x\:=\:\cancel{\frac{72}{3}}\\\\\implies\boxed{\red{\sf\:x\:=\:24}}$

By substituting x = 24 in equation ( 1 ), we get,

$\implies\:$ y = x + 12

$\implies\:$ y = 24 + 12

$\implies\boxed{\red{\sf\:y\:=\:36}}$

The numerator of the fraction ( x ) = 24

The denominator of the fraction ( y ) = 36

$\boxed{\red{\sf\:The\:required\:fraction\:=\:\frac{24}{36}}}$