IBPS PO Mains 12 Oct 2025 Shift 1 Paper

Concept:Angles in a pie chart are proportional to the number of projects, and the public-private difference helps find the total.Explanation:Let the angles for Q3 and Q4 be $y$ and $x$ respectively.Given $x - y = 21.6^\circ$ and $x + y = 360^\circ - (108^\circ + 100.8^\circ) = 151.2^\circ$.Adding: $2x = 172.8^\circ$, so $x = 86.4^\circ$ and $y = 64.8^\circ$.In Q1, private projects are $35\%$ and public projects are $65\%$.The difference is 108 projects, so $(65\% - 35\%) \times \text{Q1 total} = 108$.Thus, $30\% \times \text{Q1 total} = 108$, giving Q1 total $=360$.Angle $108^\circ$ corresponds to 360 projects, so $1^\circ = \frac{360}{108} = \frac{10}{3}$ projects.Total annual projects $= 360 \times \frac{10}{3} = 1200$.Quarterly totals: Q1 $=360$, Q2 $=100.8 \times \frac{10}{3}=336$, Q3 $=64.8 \times \frac{10}{3}=216$, Q4 $=86.4 \times \frac{10}{3}=288$.Average public projects in Q2 and Q4 is 150, so their total is 300.Let private percentages in Q2 and Q4 be $3P\%$ and $P\%$ respectively.So public percentages are $(100-3P)\%$ and $(100-P)\%$.$336 \times \frac{100-3P}{100} + 288 \times \frac{100-P}{100} = 300$.Solving: $624 - 12.96P = 300$, hence $P = 25$.Private projects: Q1 $=35\% \times 360=126$, Q2 $=75\% \times 336=252$, Q3 $=50\% \times 216=108$, Q4 $=25\% \times 288=72$.Total private projects $=126+252+108+72=558$.Answer:The total number of private projects handled during the year is $558$, i.e. option C.