Question

i recievd two salary hikes during the current financial year. The first time, my salary was hiked by x% while the second time it was hiked by 2x% .my current salary is 1.875times of my salary at the starting of the year .find the value of x​

Answer 1

Answer:

The value of x is 25.

Step-by-step explanation:

let y be the initial salary,

After hiking x%, new salary = y +x% of y

$=y+\frac{xy}{100}$

$=y(1+0.01x)$

Again after hiking 2x%, new salary = y(1+0.01x) + 2x% of y(1+0.01x)

$=y(1+0.01x) + \frac{2xy(1+0.01x)}{100}$

$=y(1+0.01x) + 0.02xy(1+0.01x)$

$=y(1+0.01x)( 1 + 0.02x)$

According to the question,

$y(1+0.01x)( 1 + 0.02x) = 1.875y$      

$(1+0.01x)( 1 + 0.02x) = 1.875$      

$1+0.02x +0.01x + 0.0002x^2 = 1.875$        

$1+0.03x + 0.0002x^2 = 1.875$      

$2x^2+ 300x + 10000 = 18750$  

$2x^2+ 300x - 8750=0$        

By quadratic formula,

x = 25 or -175

The value of x must be positive ( because the salary was hiked )

Hence, the value of x is 25.

Answer 2

Answer:

The value of x is 25

Explanation:

Let my salary was P

After first hike of x% the salry will be P + Px/100 = P(1 + x/100)

After the second hike of 2x% the salary will be

= P(1 + x/100) + P(1 + x/100)× 2x/100

= P[1 + x/100 + 2x/100 + 2x²/10000]

According to the question

P[1 + x/100 + 2x/100 + 2x²/10000] = 1.875P

$\implies  1+\frac{3x}{100} +\frac{2x^2}{10000}=1.875$

$\implies  10000+300x +2x^2=18750$

$\implies  2x^2+300x-8750=0$

$\implies  x^2+150x-4375=0$

$\implies  x^2+175x-25x-4375=0$

$\implies  x(x+175)-25(x+175)=0$

$\implies  (x+175)(x-25)=0$

$\implies  x=25, -175$

But x cannot be negative

Thus x = 25

Therefore the value of x is 25%