A sum of 3392 is divided among A, B, C and D such that the ratio for shares of A and B is 2: 5, that of B and C is 3 : 7 and that of C and D is 5 : 8. What is the share of C?

Options

A. ₹1060
B. ₹1696
C. ₹848
D. ₹840

Answer

To solve the problem of dividing the sum of Rs. 3392 among A, B, C, and D based on the given ratios, we will follow these steps:

### Step 1: Understand the Ratios
We have the following ratios:
- A : B = 2 : 5
- B : C = 3 : 7
- C : D = 5 : 8

### Step 2: Express All Ratios in Terms of a Common Variable
To combine these ratios, we need to express them in terms of a common variable.

Let:
- A = 2x
- B = 5x (from A : B)

From B : C = 3 : 7, we can express B in terms of C:
- B = 3y
- C = 7y

Setting the two expressions for B equal gives us:
5x = 3y → y = (5/3)x

Now substituting y into C:
- C = 7y = 7 * (5/3)x = (35/3)x

Next, we look at the ratio C : D = 5 : 8:
- C = 5z
- D = 8z

Setting C equal to the previous expression gives:
(35/3)x = 5z → z = (7/3)x

Now substituting z into D:
- D = 8z = 8 * (7/3)x = (56/3)x

### Step 3: Combine All Variables
Now we have:
- A = 2x
- B = 5x
- C = (35/3)x
- D = (56/3)x

### Step 4: Find Total Parts
To find the total parts, we need to convert all shares to a common denominator:
- A = 2x = (6/3)x
- B = 5x = (15/3)x
- C = (35/3)x
- D = (56/3)x

Adding these gives:
Total = (6/3)x + (15/3)x + (35/3)x + (56/3)x = (112/3)x

### Step 5: Set Up the Equation
We know the total amount is Rs. 3392:
\[ \frac{112}{3}x = 3392 \]

### Step 6: Solve for x
To find x, multiply both sides by 3:
\[ 112x = 3392 \times 3 \]
\[ 112x = 10176 \]
Now divide by 112:
\[ x = \frac{10176}{112} = 91 \]

### Step 7: Calculate the Share of C
Now we can find the share of C:
\[ C = \frac{35}{3}x = \frac{35}{3} \times 91 = \frac{3185}{3} = 1060 \]

### Final Answer
Thus, the share of C is Rs. 1060.

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