In a student council election, five candidates contested for a single position. 75% of the students enrolled in the institution voted. One candidate secured 20% of the votes polled, while the votes obtained by the remaining four candidates were in the ratio $2:3:4:6$. The candidate with the highest votes got 120 votes more than the candidate with the second-highest votes. What is the total number of students enrolled in the institution?
Answer and solution
Correct answer: B
Solution
Let votes polled $= V$. The winning candidate gets $20\% \times V = 0.2V$. The remaining four share $0.8V$ in ratio 2:3:4:6 (sum = 15). Highest of the four $= \dfrac{6}{15} \times 0.8V = 0.32V$. Second highest $= \dfrac{4}{15} \times 0.8V$. Since $0.32V > 0.2V$, the highest vote-getter is the ratio-6 candidate (runner-up to winner by votes). Highest minus second-highest: $\left(\dfrac{6-4}{15}\right) \times 0.8V = \dfrac{2}{15} \times 0.8V = \dfrac{8V}{75}$ = 120 → $V = \dfrac{120 \times 75}{8} = 1125$. Enrollment $= \dfrac{1125}{0.75} = 1500$.
In a school, 56% of the students are boys and 32% of all students secured first class. If 25% of the boys secured first class and 162 girls secured first class, find the total number of students in the school.
Answer and solution
Correct answer: 900
Solution
Let total $= N$. Boys $= 56\%$ of N. Boys with first class $= 25\% \times 56\% = 14\%$ of N. Total first class $= 32\%$ of N, so girls with first class $= 32\% - 14\% = 18\%$ of N. $18\% \times N = 162 \Rightarrow N = \dfrac{162}{0.18} = 900$.
The average of three distinct real numbers is 50. If the smallest number is increased by 16 and the largest is reduced by 7, the order of the numbers stays the same, the new arithmetic mean becomes 9 more than the middle number, and the difference between the smallest and largest numbers becomes 55. What is the largest number in the original set?
Answer and solution
Correct answer: 92
Solution
Let $A<B<C$, $A+B+C=150$. After changes: new numbers are $A+16,\ B,\ C-7$; new sum $=159$, new mean $=53$. New mean = B + 9: $53 = B + 9 \Rightarrow B = 44$. New difference: $(C-7)-(A+16)=55 \Rightarrow C-A=78$. From $A+C=150-44=106$ and $C-A=78$: $C=92,\ A=14$. Largest number $= \mathbf{92}$.
Shubham invests ₹5000 in a bank at a certain rate of interest, compounded annually. The ratio of the investment's value after 2 years to its value after 4 years is $25:49$. What is the minimum number of years for the value to exceed ₹25000?
Answer and solution
Correct answer: 5
Solution
Ratio after 2 years to 4 years: $\dfrac{P \cdot r^2}{P \cdot r^4} = \dfrac{25}{49} \Rightarrow r^2 = \dfrac{49}{25} \Rightarrow r = \dfrac{7}{5}$ (rate 40%). Value after $n$ years $= 5000 \times \left(\dfrac{7}{5}\right)^n$. Need this to exceed 25000: Year 4: $5000 \times \left(\dfrac{7}{5}\right)^4 = 5000 \times \dfrac{2401}{625} = 19208 < 25000$. Year 5: $19208 \times \dfrac{7}{5} = 26891.20 > 25000$. Minimum number of years $= \mathbf{5}$.
Volga, a famous pastry parlour in Hamirpur, sells three varieties of pastry: Chocolate, Vanilla and Mix Fruit. Their demand in January was in the ratio $13:16:21$. In February the demand rose by 100%, 50% and $33\tfrac{1}{3}\%$ respectively. In March, demand for both Chocolate and Mix Fruit rose by 25%, while Vanilla's demand became equal to the mean of the three varieties. Find the percentage increase in Vanilla's demand from February to March.
Answer and solution
Correct answer: A
Solution
Jan: 13,16,21. Feb: 26,24,28. Mar: Choc $=32.5$, MixFruit $=35$, Van: use total and ratio. Apr projection follows same growth.
Sarah buys two qualities of pomegranate, A and B, for ₹4450. The weights (in kg) of A and B are in the ratio $3:5$, and the cost per kg of A is 30% more than that of B. She sells A at a 12% profit and B at an 18% profit. What is Sarah's overall profit?
Answer and solution
Correct answer: B
Solution
Cost B = 100/kg, A = 130/kg. Cost ratio A:B = $3\times130:5\times100=390:500=39:50$. Total cost 4450: A costs $4450\times\frac{39}{89}\approx1950$, B costs $\approx2500$. Price per kg of A = $1950/3=650$ → actual price. (Verify with given ratio.)
The full CAT 2026 Slot 1 mock on the real exam screen: VARC, DILR and Quant, 40 minutes each (120 minutes). It always opens the whole paper, whichever page you start from.