Ravi and Sneha got married 10 years ago and at that time ratio of their ages was 5:4. Ratio of present age of Ravi and Sneha is 7:6. After marriage they had seven children including a triplet and a twin. The ratio of present age of triplet, twin, sixth and the seventh child is 4:3:2:1. Find the largest possible value of the present total age of the family.

Options

A. A)121
B. B)107
C. C)101
D. D)112.25

Answer

To solve the problem step-by-step, we will break it down into manageable parts.

### Step 1: Determine the ages of Ravi and Sneha 10 years ago
Let the ages of Ravi and Sneha 10 years ago be represented as:
- Ravi's age = 5x
- Sneha's age = 4x

### Step 2: Calculate their present ages
Since they got married 10 years ago, we add 10 years to their ages:
- Present age of Ravi = 5x + 10
- Present age of Sneha = 4x + 10

### Step 3: Set up the ratio of their present ages
According to the problem, the ratio of their present ages is given as 7:6. Therefore, we can set up the equation:
\[ \frac{5x + 10}{4x + 10} = \frac{7}{6} \]

### Step 4: Cross-multiply and solve for x
Cross-multiplying gives us:
\[ 6(5x + 10) = 7(4x + 10) \]
Expanding both sides:
\[ 30x + 60 = 28x + 70 \]
Rearranging gives:
\[ 30x - 28x = 70 - 60 \]
\[ 2x = 10 \implies x = 5 \]

### Step 5: Calculate the present ages of Ravi and Sneha
Substituting \(x = 5\) back into the age expressions:
- Present age of Ravi = \(5(5) + 10 = 25 + 10 = 35\)
- Present age of Sneha = \(4(5) + 10 = 20 + 10 = 30\)

### Step 6: Determine the ages of the children
The problem states they have 7 children, including a triplet and a twin. The ratio of the ages of the triplet, twin, sixth, and seventh child is given as 4:3:2:1. Let their ages be represented as:
- Triplet's age = 4y
- Twin's age = 3y
- Sixth child's age = 2y
- Seventh child's age = 1y

### Step 7: Find the maximum possible ages of the children
Since they were married 10 years ago, the maximum age for the youngest child (the triplet) can be 9 years (since they could be born just before the marriage). Thus, we set:
\[ 4y = 9 \implies y = \frac{9}{4} = 2.25 \]

### Step 8: Calculate the ages of each child
Now we can calculate the ages of each child:
- Triplet's age = \(4y = 4 \times 2.25 = 9\)
- Twin's age = \(3y = 3 \times 2.25 = 6.75\)
- Sixth child's age = \(2y = 2 \times 2.25 = 4.5\)
- Seventh child's age = \(1y = 1 \times 2.25 = 2.25\)

### Step 9: Calculate the total age of the children
Since there are three triplets, their total age contribution will be:
- Total age of triplets = \(3 \times 9 = 27\)
- Total age of twin = \(6.75\)
- Total age of sixth child = \(4.5\)
- Total age of seventh child = \(2.25\)

Total age of all children:
\[ 27 + 6.75 + 4.5 + 2.25 = 40.5 \]

### Step 10: Calculate the total age of the family
Now, we add the ages of Ravi and Sneha to the total age of the children:
\[ Total age of family = 35 + 30 + 40.5 = 105.5 \]

### Final Answer
The largest possible value of the present total age of the family is **105.5 years**.

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