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A sum of Rs. 12,384 is divided between A, B, C and D such that the ratio of the shares of A and B is 3 : 4, that of B and C is 5 : 6, and that of C and D is 8 : 9. What is the share of C ? 
  • a)
    Rs. 2,880
  • b)
    Rs. 3,888
  • c)
    Rs. 3,456
  • d)
    Rs. 2,160
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A sum of Rs. 12,384 is divided between A, B, C and D such that the rat...
Given:
A : B = 3 : 4
B : C = 5 : 6
C : D = 8 : 9
Sum to divided among them = Rs. 12,384
Concept used:
Ratio Proportion
Calculation:
A : B = 3 : 4 = 15 : 20
B : C = 5 : 6 = 20 : 24
C : D = 8 : 9 = 24 : 27
A : B : C : D = 15 : 20 : 24 : 27
Share of C = 24/(15 + 20 + 24 + 27) × 12384 = Rs. 3456
∴ The share of C is Rs. 3456.
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Community Answer
A sum of Rs. 12,384 is divided between A, B, C and D such that the rat...
Given:
- Total sum = Rs. 12,384
- Ratio of A's share to B's share = 3 : 4
- Ratio of B's share to C's share = 5 : 6
- Ratio of C's share to D's share = 8 : 9

To Find:
- Share of C

Solution:
Let's assume the shares of A, B, C, and D are 3x, 4x, 5y, and 6y respectively, where x and y are constants.

Step 1:
According to the given information,
A's share + B's share + C's share + D's share = Total sum
3x + 4x + 5y + 6y = 12,384
7x + 11y = 12,384 --(Equation 1)

Step 2:
We have the ratios:
A's share : B's share = 3 : 4
B's share : C's share = 5 : 6
C's share : D's share = 8 : 9

We can write these ratios as:
A's share/B's share = 3/4
B's share/C's share = 5/6
C's share/D's share = 8/9

Step 3:
Using the ratios, we can express A's share, B's share, and D's share in terms of C's share:
A's share = (3/4) * B's share
B's share = (5/6) * C's share
D's share = (9/8) * C's share

Step 4:
Substituting the above expressions in Equation 1, we get:
7x + 11y = 12,384
(3/4) * (5/6) * C's share + (9/8) * C's share = 12,384
(15/24) * C's share + (27/24) * C's share = 12,384
(42/24) * C's share = 12,384
C's share = (12,384 * 24) / 42
C's share = 7,056

Answer:
The share of C is Rs. 7,056, which is option C.
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A sum of Rs. 12,384 is divided between A, B, C and D such that the ratio of the shares of A and B is 3 : 4, that of B and C is 5 : 6, and that of C and D is 8 : 9. What is the share of C ?a)Rs. 2,880b)Rs. 3,888c)Rs. 3,456d)Rs. 2,160Correct answer is option 'C'. Can you explain this answer?
Question Description
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