Question

if the total of 21% of X and 20% of Y is equal to 18/19th of the total of 22% of X and 24% of Y , then what is the value of X/Y ?
(1) 52/3
(2) 1
(3) 3/52
(4) 26/3​

Answer 1

Answer:

x/y = 14

Step-by-step explanation:

Given: 21℅x + 20℅y = 18/19( 22℅x + 24℅y)

21/100 x + 20/100 y = 18/19( 22/100 x + 24/100 y)

21x + 20y = 18/19( 22x + 24y)

19( 21x + 20y) = 18( 22x + 24y)

399x + 380y = 396x + 432y

399x - 396x = 432y - 380y

3x = 52y

x/y = 52/3

= 14

Answer 2

For the given relation, the value of X/Y is 52/3. (option 1)

Given,

The total of 21% of X and 20% of Y is equal to 18/19th of the total of 22% of X and 24% of Y.

To find,

The value of X/Y.

Solution,

Firstly, we know that a percent or percentage, in mathematics is a number or ratio that is expressed per hundred.

It means, for example, if a number is, say, x percent, then it is written as x% and can be expressed as $\frac{x}{100} .$

We can see here, it is given that

(the total of 21% of X and 20% of Y) = 18/19th (the total of 22% of X and 24% of Y)

So, it can be written as,

$\frac{21}{100} X + \frac{20}{100} Y=\frac{18}{19} (\frac{22}{100}X +\frac{24}{100} Y)$

This can be simplified as follows.

$21X+20Y=\frac{18}{19} (22X + 24 Y)$

$\implies 19(21X+20Y)=18 (22X + 24 Y)$

$\implies 399X+380Y= 396X + 432Y$

$\implies 399X-396X = 432Y-380Y$

$\implies 3X=52Y$

On rearranging the above equation, taking variables on one side, we get,

$\frac{X}{Y} =\frac{52}{3} .$

Therefore, for the given relation, the value of X/Y is 52/3. (option 1)

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