1.

Rs. 3,000 is divided among A, B and C, so that A receives 1/3 as much as B and C together receive and B receives 2/3 as much as A and C together receive. Then share of C is1). Rs. 5252). Rs. 1,6253). Rs. 1,0504). Rs. 600

Answer»

Given, 3,000 is divided among A, B and C, so that A receives 1/3 as much as B and C together receive and B receives 2/3 as much as A and C together receive

$(\Rightarrow {\rm{A}} = \FRAC{1}{3}{\rm{\;}}\left( {{\rm{\;B}} + {\rm{C}}} \right))$

3A = B + C……….(1)

$(\Rightarrow {\rm{B}} = \frac{2}{3}{\rm{\;}}\left( {{\rm{\;A}} + {\rm{C}}} \right))$

⇒ 3B = 2A + 2C…………(2)

PUTTING the value of C from (1) into (2), we get,

⇒ 3B = 2 A + 2 (3A – B)

8A = 5B …………….(3)

⇒ Similarly, we can solve and will get relation between B and C.

⇒ 7B = 8C …………….. (4)

⇒ Multiplying (3) with 7 and (4) with 5, we get,

⇒ 56A = 35B = 40C

$(\Rightarrow \frac{{56{\rm{A}}}}{{280}} = \frac{{35{\rm{B}}}}{{280}} = \frac{{40{\rm{C}}}}{{280}})$

$(\Rightarrow \frac{{\rm{A}}}{5} = \frac{{\rm{B}}}{8} = \frac{{\rm{C}}}{7})$

⇒ A : B : C = 5 : 8: 7

$(\Rightarrow {\rm{Share\;of\;C}} = \frac{7}{{20}} \times 3000 = 1050)$



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