Question

The numerator of a fraction is 3 less than its denominator. If we add 1 to both numerator and denominator, it becomes equal to. Find the fraction.

Answer 1

Let the denominator be x.
then,
numerator= x-3
fraction will be x-3÷ x
After adding 1 to it.....
x-3+1÷x+1

Answer 2

Given,

The Sum of the Digits of a two Digit number is 9.

If 9 is added to the number by reversing its digits then the result is thrice the original number.

To Find,

The Two Digit Number

Solution :

$\implies$ Suppose the digit at the ten's place be x

And, Suppose the digit at the one's place be y

Therefore,

Two Digit Number = 10x + y

Reversing Number = 10y + x

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

According to the First Condition:

The sum of the digits of a two digit number is 9.

$\longrightarrow \sf${x + y = 9}⟶x+y=9

$\longrightarrow \boxed{\sf{x = 9 - y}}⟶$

x=9−y

1) Equation

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

According to the Second Condition:

If 9 is added to the number by reversing its digits,then the result is thrice the original number.

$\longrightarrow \sf{3(10x + y) = 10y + x + 9}⟶3(10x+y)=10y+x+9$

$\longrightarrow \sf${30x + 3y = 10y + x + 9}⟶30x+3y=10y+x+9

$\longrightarrow \sf[tex]{30x - x = 10y - 3y + 9}⟶30x−x=10y−3y+9</p><p></p><p>[tex]\longrightarrow \sf{29x = 7y + 9}⟶29x=7y+9</p><p></p><p>║Now Put the Value of x From the Equation First ║</p><p></p><p>[tex]\longrightarrow \sf{29(9 - y) = 7y + 9}⟶29(9−y)=7y+9</p><p></p><p>[tex]\longrightarrow \sf{261 - 29y = 7y + 9}⟶261−29y=7y+9$

$\longrightarrow \sf{261 - 9 = 7y + 29y}⟶261−9=7y+29y[/tex-]</p><p></p><p>[tex]\longrightarrow \sf{252 = 36y}⟶252=36y$

$\longrightarrow \sf{y = \dfrac{252}{36}}⟶y= </p><p>36</p><p>252$

$\longrightarrow \boxed{\sf{y = 7}}⟶ </p><p>y=7$

║Now Put the Value of y in First Equation ║

$\longrightarrow\sf{x = 9 -y}⟶x=9−y$

$\longrightarrow\sf{x = 9 - 7}⟶x=9−7$

$\longrightarrow \boxed{\sf{x = 2}}$⟶

x=2

Therefore,

$\boxed{\bold{\red{Two\: Digit\: Number = 10x + y = 10(2) + 7 = 27}}}$

Two Digit Number=10x+y=10(2)+7=27