Question

A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we
get 18/11, but if the numerator is increased by 8 and the denominator is doubled we get 2/5. Find
the fraction.​

Answer 1

Answer:

let the fraction be x/y

according to the question,

3x/y-3=18/11

cross multiply and u will get

33x=18y-54

11x=6y-18-----(1)

and

x+8/2y=2/5

5x+40=4y----(2)

solve both the equations and you will get x and y

x/y will be the fraction

Answer 2

ANSWER:-

Given:

A fraction is such that if the numerator is multiplied by 3 and the denominator is reduce by 3, we get 18/11, but if the numerator is increased by 8 and the denominator is double we get 2/5.

To find:

The fraction.

Explanation:

Let the fraction be $\frac{R}{M}$

So,

R= Numerator

M= Denominator

According to the question:

→First Case

• In numerator is multiplied by 3
• In denominator is reduce by 3
• We get 18/11

Now,

$=> \:\frac{3R}{M-3} =\frac{18}{11}$

[Cross multiplication]

$=>\: 33R= 18M-54\\\\=>33R-18M=-54\\\\=> 11R- 6M= -18\\\\=>11R= -18+6M\\\\=> R= \frac{-18+6M}{11} ...................(1)$

→Second Case

We have,

• If the numerator is increased by 8 and the denominator is double we get 2/5.

$=> \frac{R+8}{2M} = \frac{2}{5}$

[Cross multiplication]

$=> 5R+40=4M\\\\=> 5R- 4M=-40...................(2)$

Therefore,

Using substitution method:

Putting the value of R in equation (2), we get,

$=>5(\frac{-18+6M}{11} ) -4M=-40\\\\=>-90+30M-44M=-440\\\\=> -90-14M=-440\\\\=>-14M=-440+90\\\\=> -14M=-350\\\\=> M= \frac{-350}{-14} \\\\=> M= 25$

Now,

Putting the value of M in equation (1), we get;

$R=\frac{-18+6(25)}{11} \\\\R= \frac{-18+150}{11} \\\\R= \frac{132}{11} \\\\R= 12$

Thus,

The fraction is 12/25.