Question

an amount of 5600 is divided among A,B and C .The sum of the shares of B and C is equal to thrice the share of the A.The sum of the shares of A and C is equal to nine-fifths the share of B.what is the share of C.

Answer 1

Step-by-step explanation:

Total Amount = Rs.5600

$\sf \implies A + B + C = 5600....(i)$

$\sf \implies B + C = 5600 - A.....(ii)$

The sum of the shares of B and C is equal to thrice the share of the A.

$\sf \implies B + C = 3A....(iii)$

From equations (ii) and (iii)

$\sf \implies 3A = 5600 - A$

$\sf \implies 3A + A = 5600$

$\sf \implies 4A = 5600$

$\sf \implies A = \dfrac{5600}{4} = 1400$

$\sf\therefore \underline{\:\: \underline{\: Share \: of \: A = Rs.1400\:}\:\:}$

The sum of the shares of A and C is equal to nine-fifths the share of B.

$\sf \implies A + C = \dfrac{9}{5}B$

$\sf \implies A + C + B = 5600$

$\sf \implies \dfrac{9}{5}B + B = \dfrac{9}{5}B$

$\sf \implies \dfrac{9B + 5B}{5} =5600$

$\sf \implies \dfrac{14B}{5} =5600$

$\sf \implies B = \dfrac{5}{14} \times 5600$

$\sf \implies B = 2000$

$\sf\therefore \underline{\:\: \underline{\: Share \: of \: B = Rs.2000\:}\:\:}$

Now, Substitute A and B in equation (i)

$\sf \implies A + B + C = 5600$

$\sf \implies 1400 + 2000 + C = 5600$

$\sf \implies 3400 + C = 5600$

$\sf \implies C = 5600 - 3400$

$\sf \implies C = 2200$

$\dashrightarrow\large\underline{\boxed{\sf \therefore Share \: of \: C = Rs.2200}}$