Question

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

Answer 1

Answer:

C=3500

A=1750 B=1750

Step-by-step explanation:

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Answer 2

$\Large {\underline { \sf {Answer :}}}$

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

$\Large {\underline { \sf {Clarification :}}}$

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.

$\Large {\underline { \sf {Explication \; of \; steps :}}}$

Let the share of C be x.

$\longrightarrow \sf { C's \: share = x}$

★ According to the question,

$\longrightarrow \sf { B's \: share = 50 \% \; of \; C's \; share}$

$\longrightarrow \sf { B's \: share = \dfrac{50}{100}x}$

$\longrightarrow \sf { B's \: share = \dfrac{1}{2}x}$

$\longrightarrow \sf { B's \: share = \dfrac{x}{2}}$

Also,

$\longrightarrow \sf { A's \: share = 50 \% \; of \; B's \; share}$

$\longrightarrow \sf { A's \: share = \dfrac{50}{100} \times \dfrac{x}{2}}$

$\longrightarrow \sf { A's \: share = \dfrac{1}{2} \times \dfrac{x}{2} }$

$\longrightarrow \sf { A's \: share = \dfrac{x}{4} }$

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

$\longrightarrow \sf { A's \: share + B's \: share + C's \: share = 7000}$

$\longrightarrow \sf { \dfrac{x}{4} + \dfrac{x}{2} + x = 7000}$

$\longrightarrow \sf { \dfrac{x+2x + 4x}{4} = 7000}$

$\longrightarrow \sf { \dfrac{7x}{4} = 7000}$

$\longrightarrow \sf { 7x = 7000 \times 4}$

$\longrightarrow \sf { 7x = 28000 }$

$\longrightarrow \sf { x =\cancel{ \dfrac{28000}{7} }}$

$\longrightarrow \sf { x = 4000 }$

$\therefore \; \underline{ \boxed{\sf { C's \: share = Rs. \; 4000 }}} \bigstar$

And,

$\longrightarrow \sf { B's \: share = \dfrac{x}{2}}$

$\longrightarrow \sf { B's \: share = \cancel{\dfrac{4000}{2}}}$

$\therefore \; \underline{ \boxed{\sf { B's \: share = Rs. \; 2000 }}} \bigstar$

Also,

$\longrightarrow \sf { A's \: share = \dfrac{x}{4} }$

$\longrightarrow \sf { A's \: share = \cancel{\dfrac{4000}{4}}}$

$\therefore \; \underline{ \boxed{\sf { A's \: share = Rs. \; 1000 }}} \bigstar$

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