Question

some apples are divided among 4 people karan ,kiran,kumar and khanna. The ratio of number of apples given to kiran to the total number of apples given to karan and khanna is 1:2 . The ratio of the number of apples given to kumar to that remaining apples is 2:5. khanna gets 2 apples more than kiran . karan gets half number of apples that kumar gets . what is the total number of apples distributed

Answer 1

Let number of apples that Kumar gets be x

Given Karan gets half of Kumar => Karan gets x/2 apples

Let Kiran get y apples.
Khanna gets 2 more apple than Kiran

=> Khanna gets y + 2 apples.


Total number of apples that Karan and Khanna gets = x/2 + y + 2

Ratio of Kiran and total number of apples that Karan and Khanna gets = 1 : 2

=>
$\frac{y}{ \frac{x}{2} + y + 2} = \frac{1}{2} \\ \\ = > 2y = \frac{x}{2} + y + 2 \\ \\ = > 2y - y = \frac{x}{2} + 2 \\ \\ = > y = \frac{x}{2} + 2$

Now ratio of Kumar to remaining apples
= 2 : 5

Kumar gets x apple

Remaining apple = apple divided - (Karan + Khanna)

apple divided = x + y + x/2 + y + 2

Karan + Khanna = x/2 + y + 2

=>Remaining = x + y + x/2 + y + 2 - x/2 - y - 2

=> Remaining = x + y

So, Karan : Remaining = 2 : 5

=>
$\frac{x}{ x + y } = \frac{2}{5} \\ \\ = > 5x = 2x + 2y \\ \\ = > 5x - 2x = 2y \\ \\ = > 3x = 2y$
3x = 2y
but y = x/2 + 2


=>
$3x = 2y \\ \\ = > 3x = 2( \frac{x}{2} + 2) \\ \\ = > 3x = x + 4 \\ \\ = > 3x - x = 4 \\ \\ = > 2x = 4 \\ \\ = > x = \frac{4}{2} \\ \\ = > x = 2$

So x = 2

So y =
$y = \frac{x}{2} + 2 \\ \\ = > y = \frac{2}{2} + 2 \\ \\ = > y = 1 + 2 \\ \\ = > y = 3$

So total apples

=
$x + y + \frac{x}{2} + y + 2 \\ \\ = > 2 + 3 + \frac{2}{2} + 3 + 2 \\ \\ = > 10 + 1 \\ = 11$

11 apples were distributed

Answer 2

Answer:

Simplest approach will be to check which options are divisible by 7 (2+5) as it is total number of apples. Hence 21.

Step-by-step explanation:

Let Kumar = 2K

Remaining = 5K

Karan = 1 / 2 * Kumar = K

Let Kiran = x, Karan + Khanna= 2x

Khanna = 2 + Kiran = 2 + x

Remaining = Kiran + Khanna + Karan

5K = x + 2 + x + K

2K = x + 1

As 5K = 3x, by subsituting above relation,

we get x = 5

Total apples = 7K = 7 * (5+1)/2 = 21 apples