1) Some people form a joint account for one year with a condition that “each person will deposit an amount equal to the number of people in the account that month. Moreover, the person who withdraws from the account in between will get their amount at the end of the year. After 6 months, 25% of the people withdrew, and 33.33% of the remaining withdrew after 3 months. At the end of the year, there was an amount of ₹4860 in their account before paying off the withdrawn amounts. Find the number of people in the beginning of the year.

• (a) 12
• (b) 24
• (c) 36
• (d) None of these

2) Consider a big cube formed of 64 smaller cubes of which 40 are coloured. The smaller cubes are arranged such that the exposure of the coloured cubes to the outside is minimized. What is the percentage of the exposed area that is coloured?

• (a) 62.5%
• (b) 50%
• (c) 41.6%
• (d) None of these

3) On May 1, 2025, a person sold all his investments for ₹108,000, incurring a loss of 10% with respect to the previous month. On April 1, 2025, he had invested all his money in shares, which represented a 20% increase over the sum he had on March 1, 2025, which represented a 20% decrease over the money he had on February 1, 2025, which represented a 25% increase over the money he had on January 1, 2025. The person had maximum money in:

• (a) February, 2025
• (b) January, 2025
• (c) April, 2025
• (d) None of these

4) The owner of a flower shop follows a particular pattern for his business. During a period of inflation, he raises his price by P%, and during a slowdown, he decreases his existing prices by P%. After a year in which there was inflation first, followed by a slowdown, the cost of a red-rose bouquet decreases by ₹162. After another year, in which there was inflation once more followed by a slowdown, the cost of this bouquet reduced by a further ₹147.42. What was the original price of the red-rose bouquet?

• (a) ₹1500
• (b) ₹1000
• (c) ₹1800
• (d) ₹1111

5) In Ranchi, only two newspapers Dainik Jagran and Prabhat Khabar are published. It is known that 25% of the city population reads Dainik Jagran and 20% reads Prabhat Khabar, whereas 8% reads both Dainik Jagran and Prabhat Khabar. It is also known that 30% of those who read Dainik Jagran but not Prabhat Khabar look into advertisement and 40% of those who read Prabhat Khabar but not Dainik Jagran look into advertisements, whereas 50% of those who read both Dainik Jagran and Prabhat Khabar look into advertisements. What is the percentage of the population who read an advertisement?

• (a) 10.8%
• (b) 11.3%
• (c) 13.9%
• (d) 12.7%

6) In D-segment car market, only three competitors (Honda, Toyota, and Hyundai) exist. Last year, the sales of Toyota were 10% more than Honda. In a year, both the firms Honda and Toyota increased their respective sales by 20%. This year, the sales of Toyota are five times that of Hyundai. How much were the sales of the firm Hyundai last year, if the total sales remained constant over the two years period?

• (a) 46%
• (b) 25%
• (c) 40.33%
• (d) 38.67%

7) Chintu is given a quadratic equation \( ax^2 + bx + c = 0 \) and is asked to make another quadratic equation from this with \( a = 1 \). In addition, one root of the second quadratic equation is same as one of the roots of the first equation but opposite in sign and the other root of the second equation is two times the second root of the first equation. Find the percentage change in the constant term of the second equation as compared to the first equation?

• (a) 200% increase
• (b) 300% decrease
• (c) 400% increase
• (d) 100% decrease

8) There are two investment schemes offered by two different financial institutions X and Y as follows:
Scheme X: Rate of interest = 10% per annum and period of maturity = 2 years
Amount is returned with compound interest compounded annually.
Scheme Y: Rate of interest = 11% per annum, amount is returned with simple interest.
For what duration, should I invest ₹25,000 in scheme Y, so as to get same amount in return if I had invested in scheme X?

• (a) \( \frac{21}{11} \) Years
• (b) \( \frac{31}{11} \) Years
• (c) \( \frac{19}{7} \) Years
• (d) \( \frac{19}{7} \) Years