District XYZ has 50,000 voters; out of them, 20% are urban voters and 80% rural voters. For an election, 25% of the rural voters were shifted to the urban area. Out of the voters in both rural and urban areas, 60% are honest, 70% are hardworking, and 35% are both honest and hardworking.

Two candidates, A and B, contested the election. Candidate B swept the urban vote, while Candidate A found favour with the rural voters. Voters who were both honest and hardworking voted for NOTA. How many votes were polled in favour of candidate A, candidate B and NOTA, respectively?

Given:

District XYZ has 50,000 voters; out of them, 20% are urban voters and 80% rural voters.

Calculation:

Total votes = 50000

⇒ Urban votes originally = 20/100 × 50000 = 10000 and Rural votes originally = 80/100 × 50000 = 40000

For election, 25% of the rural voters were shifted to the urban area 

⇒ 25/100 × 40000 = 10000 rural votes shifted to urban area.

⇒ Now, Urban votes = 10000 + 10000 = 20000 and Rural votes = 40000 - 10000 = 30000

Out of the voters in both rural and urban areas, 60% are honest, 70% are hardworking, and 35% are both honest and hardworking.

Voters who were both honest and hardworking voted for NOTA.

∴ Votes swept by NOTA = 35% of urban + 35% of rural =  35/100 × 20000 + 35/100 × 30000 = 17500 

Candidate A found favour with the rural voters, rural voters left = 100% - 35% = 65% of rural voters

∴ Votes swept by A =  65/100 × 30000 = 19500

Candidate B found favour with the urban voters, Urban voters left = 100% - 35% = 65% of urban voters

∴ Votes swept by B =  65/100 × 20000 = 13000

⇒ Votes polled in favor of candidate A, candidate B and NOTA are 19500, 13000 and 17500 respectively