IBPS PO Mains 30 Nov 2024 Shift 2 Paper

Concept:Profit depends on the number of items sold and the difference between the actual market price and the cost price.First, obtain the missing values $r$, $w$, and $z$ from the pie-chart conditions, then use the profit equality to find the required cost price.Explanation:The single-digit primes are $2, 3, 5, 7$. Since $r$ is a product of two distinct single-digit primes and one factor is $3$, the possible values are $3 \times 5 = 15$ and $3 \times 7 = 21$. Given $w + r = 33$ and $w > r$. If $r = 21$, then $w = 12$, which is not greater than $21$. So this case is invalid. If $r = 15$, then $w = 18$, and indeed $18 > 15$. Hence $r = 15$ and $w = 18$. Now use the pie-chart angles: $P = 72^\circ$ and $S = (180 - w)^\circ = 162^\circ$. The remaining angle for $Q$ and $R$ is $360^\circ - (72^\circ + 162^\circ) = 126^\circ$. This represents $\frac{126}{360} \times 100 = 35\%$ of the total items. Given $Q = z\%$ and $R = (z - r)\%$, we get $z + (z - 15) = 35$, so $2z = 50$ and $z = 25$. Total items bought by all buyers $= 20{,}000$. $P$ gets $20\%$, so items with $P = 4{,}000$. For $P$, $A : B = 3 : 2$, hence $A = 2{,}400$ and $B = 1{,}600$. $Q$ gets $25\%$, so items with $Q = 5{,}000$. For $Q$, the percentage of item $A = (2r + z)\% = (30 + 25)\% = 55\%$. Thus item $A$ for $Q = 55\%$ of $5{,}000 = 2{,}750$, and item $B$ for $Q = 2{,}250$. From the given line graph, the actual market price of item $A$ for $P$ in 2013 is $\text{Rs. }280$. Given the cost price of item $A$ for $P$ in 2013 is $\text{Rs. }250$. Profit per item $= 280 - 250 = \text{Rs. }30$. Total profit of $P$ on item $A$ in 2013 $= 2{,}400 \times 30 = \text{Rs. }72{,}000$. This profit is equal to the total profit of $Q$ on item $B$ in 2015. From the line graph, the actual market price of item $B$ for $Q$ in 2015 is $\text{Rs. }320$. Let the required cost price be $x$. $2{,}250 \times (320 - x) = 72{,}000$. So $320 - x = \frac{72{,}000}{2{,}250} = 32$. Hence $x = 320 - 32 = 288$.Answer:The cost price of item $B$ for $Q$ in 2015 was $\text{Rs. }288$. Correct option: C.