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 other four share $80\%$ of $V$ in the ratio $2:3:4:6$ (total 15). Highest $= 80\% \times \tfrac{6}{15} = 32\%$ of $V$; second-highest $= 80\% \times \tfrac{4}{15} = \tfrac{64}{3}\%$ of $V$ Difference $= \tfrac{32}{3}\%$ of $V = 120 \Rightarrow V = 1125$ $75\%$ of enrolled $= 1125 \Rightarrow$ enrolled $= 1500$
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 $= 25\%$ of $56\% = 14\%$ of $N$ Girls with first class $= 32\% - 14\% = 18\%$ of $N = 162$ $N = \dfrac{162 \times 100}{18} = 900$
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 the numbers be $A < B < C$. $A + B + C = 150$. New sum $= (A + 16) + B + (C - 7) = 159$, new mean $= 53$ Mean is 9 more than the middle number: $B = 53 - 9 = 44$ $A + C = 106 \Rightarrow A = 106 - C$ $(C - 7) - (A + 16) = 55 \Rightarrow C - 7 - 106 + C - 16 = 55$ $2C = 184 \Rightarrow C = 92$
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
Growth over 2 years $= \dfrac{49}{25}$, so annual growth factor $= \dfrac{7}{5}$, i.e. $40\%$ a year. Year 1: ₹7000 · Year 2: ₹9800 · Year 3: ₹13720 · Year 4: ₹19208 · Year 5: ₹26891.20 It first exceeds ₹25000 after $5$ years.
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.
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
Take cost of B $= ₹100$/kg, so A $= ₹130$/kg. Cost ratio A : B $= 3 \times 130 : 5 \times 100 = 39 : 50$ A $= 4450 \times \tfrac{39}{89} = ₹1950$; B $= 4450 \times \tfrac{50}{89} = ₹2500$ Profit $= 12\%$ of 1950 $+ 18\%$ of 2500 $= 234 + 450 = ₹684$
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.