Question

There are 4 friends - Ajay, Rahul, Raj, Zaheer who invested money in stocks. After couple of years they made profit and decided to split money amongst them. Out of total Ajay gets a%. From the amount left after Ajay takes his share, Rahul gets b%. Raj then gets c% of remaining amount and Zaheer gets the remaining balance. The amount Zaheer got is a% less than Ajay’s. Rahul and Raj got same amount. b = 2a. Figure what percentage of Ajay’s amount did Raj get ?

Answer 1

Answer:

50%

Step-by-step explanation:

Answer 2

Given:

Ajay gets a%

Rahul gets b% of the remaining.

Raj gets c% o the remaining.

Zaheer gets the remaining, which is also a% less than Ajay.

Rahul and Raj get the same amount, which is also 2a each

To Find:

The percentage of Ajay's amount is Raj's amount

Solution

Find the amount Rahul gets in term of a:

Given that b = 2a

Rahul gets 2a% of the remaining of Ajay.

$\text{Rahul} = \dfrac{2a}{100} \times (100 - a)$

$\text{Rahul} = \dfrac{2a(100 - a)}{100}$

$\text{Rahul} = \dfrac{200a - 2a^2}{100}$

$\text{Rahul} = 2a - 0.02a^2$

Find the amount Raj gets in term of a:

$\text{Raj} = \text{Rahul}$

$\text{Raj} = 2a - 0.02a^2$

Find the amount Zaheer gets:

Zaheer got is a% less than Ajay.

$\text{Zaheer} = a - (\dfrac{a}{100} \times a)$

$\text{Zaheer} = a - \dfrac{a^2}{100}$

$\text{Zaheer} = a - 0.01a^2$

Solve a:

All the percentage must add up to 100%

$a + ( 2a - 0.02a^2) + ( 2a - 0.02a^2) + (a - 0.01a^2) = 100$

$a + 2a - 0.02a^2 + 2a - 0.02a^2 + a - 0.01a^2 = 100$

$6a - 0.05a^2 = 100$

$0.05a^2 - 6a + 100 = 0$

$5a^2 - 600a + 10000 = 0$

$5(a - 20) (a - 100) = 0$

$a = 20 \text { or } a = 100 \text{(Rejected)}$

Find the percentage that Ajay get:

$\text{Ajay} = a$

$\text{Ajay} = 20\%$

Find the percentage that Raj get:

$\text{Raj} = 2a - 0.02a^2$

$\text{Raj} = 2(20) - 0.02(20)^2$

$\text{Raj} = 32\%$

Find the percentage of Ajay's amount is Raj's amount:

$\text{Percentage of Raj} = \dfrac{\text{Raj}}{\text{Ajay}} \times 100$

$\text{Percentage of Raj} = \dfrac{\text{32}}{\text{20}} \times 100$

$\text{Percentage of Raj} = 160\%$

Answer: Raj gets 160% of what Ajay got.