Divide₹7000among A, Band C such that A gets 50℅ of What B gets and B gets 50℅ of what C gets​

2 thoughts on “Divide₹7000among A, Band C such that A gets 50℅ of What B gets and B gets 50℅ of what C gets​”

1. [tex] \Large {\underline { \sf {Answer :}}}[/tex]

   • A’s share = ₹ 1000
   • B’s share = ₹ 2000
   • C’s share = ₹ 4000

   [tex] \Large {\underline { \sf {Clarification :}}}[/tex]

   Here, we are provided that total amount is ₹7000. We are asked to divide ₹7000 among A, B and C in such a way that A gets 50% of share of B and B gets 50% of share of C.

   Required Steps :

   Step 1 : We’ll first assume C’s share as ₹ x.

   Step 2 : Then, we’ll write the share of B in the terms of C’ share. Similarly, we’ll write the share of A in the terms of B’ share.

   Step 3 : Since, the total amount we have to divide is 7000. So, by forming a suitable equation, we’ll find the value of x (C’s share).

   Step 4 : After finding the value of x, we’ll substitute in the expressions of the shares of A and B to find their share.

   [tex] \Large {\underline { \sf {Explication \; of \; steps :}}}[/tex]

   Let the share of C be x.

   [tex] \longrightarrow \sf { C’s \: share = x} [/tex]

   ★ According to the question,

   [tex] \longrightarrow \sf { B’s \: share = 50 \% \; of \; C’s \; share} \\[/tex]

   [tex] \longrightarrow \sf { B’s \: share = \dfrac{50}{100}x} \\[/tex]

   [tex] \longrightarrow \sf { B’s \: share = \dfrac{1}{2}x} \\[/tex]

   [tex] \longrightarrow \sf { B’s \: share = \dfrac{x}{2}} \\[/tex]

   Also,

   [tex] \longrightarrow \sf { A’s \: share = 50 \% \; of \; B’s \; share} \\[/tex]

   [tex] \longrightarrow \sf { A’s \: share = \dfrac{50}{100} \times \dfrac{x}{2}} \\[/tex]

   [tex] \longrightarrow \sf { A’s \: share = \dfrac{1}{2} \times \dfrac{x}{2} } \\[/tex]

   [tex] \longrightarrow \sf { A’s \: share = \dfrac{x}{4} } \\[/tex]

   Now, as we know that total amount to be distributed among A,B and C is ₹ 7000. So,

   [tex] \longrightarrow \sf { A’s \: share + B’s \: share + C’s \: share = 7000} \\[/tex]

   [tex] \longrightarrow \sf { \dfrac{x}{4} + \dfrac{x}{2} + x = 7000} \\[/tex]

   [tex] \longrightarrow \sf { \dfrac{x+2x + 4x}{4} = 7000} \\[/tex]

   [tex] \longrightarrow \sf { \dfrac{7x}{4} = 7000} \\[/tex]

   [tex] \longrightarrow \sf { 7x = 7000 \times 4} \\[/tex]

   [tex] \longrightarrow \sf { 7x = 28000 } \\[/tex]

   [tex] \longrightarrow \sf { x =\cancel{ \dfrac{28000}{7} }} \\[/tex]

   [tex] \longrightarrow \sf { x = 4000 } \\[/tex]

   [tex] \therefore \; \underline{ \boxed{\sf { C’s \: share = Rs. \; 4000 }}} \bigstar \\ [/tex]

   And,

   [tex] \longrightarrow \sf { B’s \: share = \dfrac{x}{2}} \\[/tex]

   [tex] \longrightarrow \sf { B’s \: share = \cancel{\dfrac{4000}{2}}} \\[/tex]

   [tex] \therefore \; \underline{ \boxed{\sf { B’s \: share = Rs. \; 2000 }}} \bigstar \\ [/tex]

   Also,

   [tex] \longrightarrow \sf { A’s \: share = \dfrac{x}{4} } \\[/tex]

   [tex] \longrightarrow \sf { A’s \: share = \cancel{\dfrac{4000}{4}}} \\[/tex]

   [tex] \therefore \; \underline{ \boxed{\sf { A’s \: share = Rs. \; 1000 }}} \bigstar \\ [/tex]

   Therefore, share of A,B and C are ₹1000, ₹2000 and ₹4000.

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2. Answer:

   C=3500

   A=1750 B=1750

   Step-by-step explanation:

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