Question

Rita and Gita are two sisters, and their ages are 8 years and 12 years respectively. One day, their mother gives Rs. 500 and asked to divide it in the ratio of their ages.

(a) How much money each of them receives?

(b) How much is the percentage Gita receives more Rita ?​

Answer 1

Answer:

a) Rita receives Rs. 200 and Gita receives Rs. 300.

b) Gita receives 50% more than Rita.

Step-by-step explanation:

To solve this problem, we'll use the concept of ratios.

The ratio of Rita's age to Gita's age is $8:12$ or simplified to $2:3$.

This means for every 2 parts Rita gets, Gita gets 3 parts.

(a) To find out how much money each of them receives:

Let's denote Rita's share as $2x$ and Gita's share as $3x$, where $x$ is a constant multiplier.

Given that the total amount is Rs. 500, we can set up the equation:

$2x + 3x = 500$

Combining like terms:

$5x = 500$

Now, solve for $x$:

$x = \dfrac{500}{5}$

$x = 100$

Now we can find Rita's share:

$\sf Rita's\; share = 2x = 2 \times 100 = 200$

And Gita's share:

$\sf Gita's\; share = 3x = 3 \times 100 = 300$

So, Rita receives Rs. 200 and Gita receives Rs. 300.

(b) To find out the percentage Gita receives more than Rita:

Gita receives Rs. 300 and Rita receives Rs. 200.

The difference in their amounts is $300 - 200 = 100$.

To find the percentage that Gita receives more than Rita, we'll use the formula:

$\textsf{Percentage} = \left( \dfrac{\textsf{Difference}}{\textsf{Rita's share}} \right) \times 100\%$

$\textsf{Percentage} = \left( \dfrac{100}{200} \right) \times 100\% \\\\ = \dfrac{1}{2} \times 100\% \\\\= 50\%$

So, Gita receives 50% more than Rita.