Question

A sum of Rs.1300 is divided between A,B,C and D, such that A's share/B's share=B's share/C's share=C's share/D's share=2/3.Then A's share is?

Answer 1

A sum of Rs.1300 is divided between A,B,C and D, such that A's share/B's share=B's share/C's share=C's share/D's share=2/3.Then A's share is

Rs. 160

• Given,
• A/B = 2/3
• ⇒ 3A = 2B
• ⇒ B = 3/2 A
• ∴ B = 3/2 A
• B/C = 2/3
• ⇒ 3B = 2C
• ⇒C = 3/2B = 3/2 (3/2 A) = 9/4 A
• ∴ C = 9/4 A
• C/D = 2/3
• ⇒ 3C = 2D
• ⇒ D = 3/2C = 3/2 (9/4 A) = 27/8 A
• ∴ D = 27/8 A
• We know that,
• A+B+C+D = 1300
• A + 3/2 A + 9/4 A + 27/8 A = 1300
• A ( 1 + 3/2 + 9/4 + 27/8 ) = 1300
• A (8.125) = 1300
• A = 160
• ∴ A = Rs. 160

Answer 2

A's share is 160.

To find :  A's share.

Given : A sum of Rs. 1300 is divided between A, B, C and D.

Such that (A's share/B's share) = (B's share/C's share) = (C's share/ D's share) =$\frac{2}{3}$.

       $\frac{A}{B}=\frac{B}{C}=\frac{C}{D}=\frac{2}{3}$

       3 A = 2 B

       3 B = 2 C

       3 C = 2 D

B = $\frac{3}{2}$ A

C = $\frac{3}{2}$ B =  

D = $\frac{3}{2}$ C =  

Given that, sum of A, B, C, D is Rs. 1300.                                     A + B + C + D = 1300  -----> (1)

Substitute the values of B, C and D in the equation (1), we get

A +  $\frac{3}{2}$ A +  $\frac{9}{4}$ A +  $\frac{27}{8}$ A = 1300

Take common term "A".

A (1+ $\frac{3}{2}$ +  $\frac{9}{4}$ + $\frac{27}{8}$ ) = 1300

A($\frac{8+12+18+27}{8}$) = 1300

A(8+12+18+27) = 1300 × 8

65 A = 10400

A =$\frac{10400}{65}$

A = 160

A's share is 160.

To learn more...

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