2/5 of the voters promise to vote for Mulayam Singh and rest promise to vote Mayawati. On election day `15%` of the voters went back on their promise to vote for Mulayam Singh & `25%` of thevoters went back on their promise to vote for Mayawati. Mayawati won by 1500 votes. Find the total number of voters.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the total number of voters
Let the total number of voters be \( x \).

### Step 2: Determine the number of voters for each candidate based on promises
According to the problem, \( \frac{2}{5} \) of the voters promised to vote for Mulayam Singh (M) and the rest promised to vote for Mayawati (Y).

- Voters for Mulayam Singh:
\[ M = \frac{2}{5}x \]

- Voters for Mayawati:
\[ Y = x - M = x - \frac{2}{5}x = \frac{3}{5}x \]

### Step 3: Calculate the number of voters who actually voted
On election day, 15% of the voters who promised to vote for Mulayam Singh went back on their promise. Therefore, the number of voters who actually voted for Mulayam Singh is:
\[ \text{Voters for M on election day} = M - 0.15M = 0.85M = 0.85 \times \frac{2}{5}x = \frac{17}{100}x \]

For Mayawati, 25% of the voters who promised to vote for her went back on their promise. Therefore, the number of voters who actually voted for Mayawati is:
\[ \text{Voters for Y on election day} = Y - 0.25Y = 0.75Y = 0.75 \times \frac{3}{5}x = \frac{9}{20}x \]

### Step 4: Set up the equation based on the winning margin
According to the problem, Mayawati won by 1500 votes. This means:
\[ \text{Votes for Y} - \text{Votes for M} = 1500 \]
Substituting the expressions we found:
\[ \frac{9}{20}x - \frac{17}{100}x = 1500 \]

### Step 5: Find a common denominator and solve for \( x \)
The common denominator for 20 and 100 is 100. Therefore, we rewrite the equation:
\[ \frac{45}{100}x - \frac{17}{100}x = 1500 \]
Combine the fractions:
\[ \frac{45x - 17x}{100} = 1500 \]
\[ \frac{28x}{100} = 1500 \]
Multiply both sides by 100:
\[ 28x = 150000 \]
Now, divide by 28:
\[ x = \frac{150000}{28} = 5357.14 \]

Since the number of voters must be a whole number, we can round to the nearest whole number, which is \( 5357 \).

### Step 6: Conclusion
The total number of voters is approximately \( 5357 \).