QuestionRs. 5214 is shared among $A, B,$ and $C$ where $A$ gets $25\%$ more than $B$ and $20\%$ more than $C$ . Find $A$ 's share.

Studdy Solution

STEP 1

Assumptions1. The total amount is Rs.5214. A gets25% more than B3. A gets20% more than C

STEP 2

Let's denote the amount B gets as $x$ . Therefore, A gets25% more than B, which is $1.25x$ . Similarly, A gets20% more than C, which means C gets $A/1.2$ .

STEP 3

Now, we can write an equation for the total amount, which is the sum of the amounts A, B, and C get.
$Total\, amount = A + B + C$

STEP 4

Substitute the expressions for A, B, and C into the equation.
$Total\, amount =1.25x + x + \frac{1.25x}{1.2}$

STEP 5

implify the equation.
$Total\, amount =2.25x + \frac{1.25x}{1.2}$

STEP 6

Now, we can solve this equation for $x$ . First, let's multiply all terms by1.2 to get rid of the fraction.
$1.2 \times Total\, amount =1.2 \times2.25x +1.25x$

STEP 7

implify the equation.
$1.2 \times Total\, amount =2.7x +1.25x$

STEP 8

Combine like terms.
$1.2 \times Total\, amount =3.95x$

STEP 9

Now, solve the equation for $x$ by dividing both sides by3.95.
$x = \frac{.2 \times Total\, amount}{3.95}$

STEP 10

Substitute the given total amount into the equation to find the value of $x$ .
$x = \frac{.2 \times5214}{3.95}$

STEP 11

Calculate the value of $x$ .
$x \approx1584$

STEP 12

Now that we have the value of $x$ , we can find the amount A gets, which is $.25x$ .
$A =.25x$

STEP 13

Substitute the value of $x$ into the equation to find the amount A gets.
$A =.25 \times158$

STEP 14

Calculate the amount A gets.
$A \approx1980$ So, A will get approximately Rs.1980. The correct answer is (e) None of these.

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