Question

An amount is to be divided between a b and c in the ratio 2:3:5 respectively.If c gives 200 of his share to b the ratio among a b and c becomes 3:5:4 what is the total sum

Answer 1

2x, 3x + 200, 5x – 200

2x/(3x + 200) = 3/5,

we will get x = 600,

so total amount = 10*600 = 6000

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Answer 2

Given :

The amount divided among a , b , c in the ratio 2 : 3 : 5

c gives 200 of his share to b the ratio among a b and c becomes 3 : 5 : 4

To Find :

The total sum of amount

Solution :

a : b : c = 2 :  3 : 5

Let The amount of a = 2 x

The amount of b = 3 x

The amount of c = 5 x

Now,

c gives 200 of his share to b the ratio among a b and c becomes 3 : 5 : 4

i.e  2 x : ( 3 x + 200 ) : ( 5 x - 200 ) = 3 : 5 : 4

Or,    $\dfrac{2x}{3x+200}$ = $\dfrac{3}{5}$

By cross multiplication

5 × 2 x = 3 × ( 3 x + 200 )

Or,  10 x = 9 x + 600

Or,   10 x - 9 x = 600

∴          x = 600

So, The sum of total amount = 2 x + 3 x + 5 x

                                                = 10 x

                                                = 10 × 600

                                                = 6000

Hence, The sum of total amount is rs 6000    Answer