Masters' Union MUSAT · Paper 5

A campus merchandise team divides 960 wristbands between two clubs, Alpha and Beta, in the ratio $5 : 7$. Later, Beta gives 80 wristbands to Alpha for a joint event. What is the new ratio of wristbands with Alpha to Beta?

The visibility impact of a digital billboard is directly proportional to its screen area and inversely proportional to the square of its distance from the viewer. Billboard A has area 18 sq. m and is 30 m away. Billboard B has area 32 sq. m and is 40 m away. What is the ratio of the visibility impact of B to that of A?

A creator’s reel views over 6 days form a geometric progression. The views on the first three days are 6, 18, and 54 respectively. What is the total number of views over all 6 days?

A student merchandise team finds that if they sell $x$ hoodies, their profit in rupees is given by $P = x(120 - x) - 800$. What is the maximum possible profit?

A coffee subscription startup finds that if it charges ₹$p$ per trial pack, it can sell $(120 - 2p)$ packs in a day. What is the maximum daily revenue it can earn?

A bar graph shows quarterly sales of two campus merchandise items, EcoCup and SmartBottle, in units. In Q1, EcoCup sold 420 and SmartBottle sold 450. In Q2, EcoCup sold 480 and SmartBottle sold 540. In Q3, EcoCup sold 520 and SmartBottle sold 510. In Q4, EcoCup sold 560 and SmartBottle sold 600. What was the total EcoCup sales in the quarters where SmartBottle sales were more than 500 units?

A bar graph for a creator-commerce startup shows quarterly revenue in ₹ lakh. Each quarter’s bar is split into two parts: “Subscription Revenue” and “One-time Purchase Revenue.” The values are: Q1: Subscription 18, One-time 12; Q2: Subscription 24, One-time 16; Q3: Subscription 30, One-time 14; Q4: Subscription 22, One-time 20. By how much is the total Subscription Revenue in Q2 and Q3 more than the total One-time Purchase Revenue in Q1 and Q4?

A bar graph shows quarterly subscriptions for a learning platform, split into Basic and Pro plans. Q1: Basic 120, Pro 80; Q2: Basic 150, Pro 110; Q3: Basic 130, Pro 160; Q4: Basic 170, Pro 140. What is the total number of subscriptions in the quarters where total subscriptions exceeded 280?

A stacked bar graph shows the quarterly sales of a D2C snack brand through Online and Retail channels. The values are: Q1 - Online ₹18 lakh, Retail ₹22 lakh; Q2 - Online ₹24 lakh, Retail ₹20 lakh; Q3 - Online ₹28 lakh, Retail ₹30 lakh; Q4 - Online ₹35 lakh, Retail ₹25 lakh. What is the total Online sales in the quarters where Retail sales were higher than Online sales?

A grouped bar graph shows revenue, in ₹ lakh, from two sources for a student marketplace startup across four quarters. The Sponsorship bars are: Q1 = 48, Q2 = 55, Q3 = 70, Q4 = 60. The Ticket Sales bars are: Q1 = 32, Q2 = 45, Q3 = 50, Q4 = 40. By how much is the total Sponsorship revenue in Q2 and Q3 greater than the total Ticket Sales revenue in Q1 and Q4?

A pie chart shows the ₹18,00,000 budget of a student-led business summit. The angles are: Venue = $90^\circ$, Marketing = $72^\circ$, Tech Setup = $54^\circ$, Prizes = $108^\circ$, and Logistics = $36^\circ$. By how much does the combined allocation for Venue and Prizes exceed the allocation for Marketing?

A Masters’ Union entrepreneurship fair packed 210 welcome boxes for three types of guests. Each startup team received 3 boxes, each investor received 2 boxes, and each volunteer received 1 box. There were 34 startup teams at the fair. The number of investors was exactly half the number of volunteers. If all 210 boxes were distributed and no boxes were left, how many volunteers were there?

Four numbers are given below. Three of them share a common property, while one does not. Choose the odd one out.

A student starts from the main gate of campus and walks 6 km east, then 8 km north, then 3 km east, then 4 km south, and finally 12 km west to reach the library. What is the shortest distance and direction of the library from the main gate?

In a campus treasure-hunt game, each of three players, Tara, Uday and Vani, has been secretly told either to always tell the truth or to always lie. They make these statements.

Tara: Exactly two of us three are telling the truth.

Uday: Tara is lying.

Vani: At least one of us three is lying.

Who is telling the truth?

During a Masters’ Union orientation queue, Rohan is 18th from the left and also 21st from the right. How many students are standing in the queue?