Question

The ratio of the monthly salaries of X and Y is 7:8.If the salary of X increased by one fifth and the salary of Y increased by one sixth, then what is the ratio of the new salary of X to that of Y?

Answer 1

Concept Introduction:

The ratio of new salary of X and Y will be increased amount of money added to the ratio of previous salary.

Given: The ratio of the monthly salaries of X and Y is $7:8$. If the salary of X increased by one fifth and the salary of Y increased by one sixth

To Find:

We have to find the value of, ratio of new salary of X and Y.

Solution:

According to the problem,

let the monthly salary x be $7x$ and $8y$

if the salary of x increased by $x/5$.

then salary of $x=36x/5$

if the salary of y increased by $y/6$

then the salary of $y =49y/6$

ratio of salary of x and y = $\frac{36x}{5} *\frac{6}{49y} =\frac{36*6}{5*49}* \frac{x}{y} =\frac{36*6}{5*49}*\frac{7}{8}$$=27:35$

Final Answer:

The value of new salary of X and Y is in ratio $27:35$.

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Answer 2

Answer:

The ratio of the new salary of X to Y is $9:10$.

Step-by-step explanation:

Step 1 of 3

Let the common ratio be $z$.

According to the question,

The ratio of the monthly salaries of X and Y = 7:8

⇒ X/Y = 7/8

⇒ X = 7$z$ and Y = 8$z$

Step 2 of 3

The salary of X is increased by one-fifth, i.e.,

X = $7z+\frac{7z}{5}$

   = $\frac{35z+7z}{5}$

   = $\frac{42z}{5}$

So, the new salary of X is $42z/5$.

Also, the salary of Y is increased by one-sixth, i.e.,

Y = $8z+\frac{8z}{6}$

   = $\frac{48z+8z}{6}$

   = $\frac{56z}{6}$

So, the new salary of Y is $56z/6$.

Step 3 of 3

The ratio of the new salary of X to Y is,

= (The new salary of X)/(The new salary of Y)

= $\frac{42z/5}{56z/6}$

= $\frac{42z}{5}\times\frac{6}{56z}$

= $\frac{21\times6}{5\times28}$

= $\frac{9}{10}$

= 9:10

Final answer: The ratio of the new salary of X to Y is $9:10$.

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