`3/7` of monthly income of Neeraj is half the monthly income of Ankur . If Soniya expend 20 % of her monthly income on Rent which is Rs 17500 and Soniya's expenditure on rent is 50 % of monthly income of Neeraj .Find ratio between monthly income of Soniya to monthly income of Ankur ?

Options

A. A)`35:12`
B. B)`35:14`
C. C)`36:17`
D. D)`37:15`

Answer

To solve the problem step-by-step, we need to find the ratio between the monthly income of Soniya and Ankur based on the information provided.

### Step 1: Set up the equations for Neeraj and Ankur's incomes.
Let Neeraj's monthly income be \( N \) and Ankur's monthly income be \( A \). According to the problem, we have:
\[ \frac{3}{7}N = \frac{1}{2}A \]
From this equation, we can express the ratio of Neeraj's income to Ankur's income:
\[ N = \frac{7}{3} \cdot \frac{1}{2}A = \frac{7}{6}A \]
Thus, the ratio of Neeraj's income to Ankur's income is:
\[ \frac{N}{A} = \frac{7}{6} \]

### Step 2: Set up the equations for Soniya's income.
Let Soniya's monthly income be \( S \). The problem states that Soniya spends 20% of her income on rent, which is Rs 17,500. Therefore:
\[ 0.2S = 17500 \]
To find Soniya's income \( S \):
\[ S = \frac{17500}{0.2} = 87500 \]

### Step 3: Relate Soniya's rent expenditure to Neeraj's income.
It is given that Soniya's expenditure on rent is 50% of Neeraj's monthly income:
\[ 17500 = 0.5N \]
From this, we can express Neeraj's income \( N \):
\[ N = 2 \times 17500 = 35000 \]

### Step 4: Substitute Neeraj's income into the ratio with Ankur's income.
Now we know \( N = 35000 \). We can substitute this into the ratio we found earlier:
\[ \frac{N}{A} = \frac{7}{6} \implies \frac{35000}{A} = \frac{7}{6} \]
Cross-multiplying gives:
\[ 7A = 6 \times 35000 \]
\[ A = \frac{210000}{7} = 30000 \]

### Step 5: Find the ratio of Soniya's income to Ankur's income.
Now we have:
- Soniya's income \( S = 87500 \)
- Ankur's income \( A = 30000 \)

To find the ratio of Soniya's income to Ankur's income:
\[ \frac{S}{A} = \frac{87500}{30000} \]
Simplifying this ratio:
\[ \frac{S}{A} = \frac{875}{300} = \frac{35}{12} \]

### Final Answer:
The ratio of Soniya's monthly income to Ankur's monthly income is:
\[ \boxed{35:12} \]