Masters' Union MUSAT · Paper 9

In a 1 km race, Aman beats Bhuvan by 40 m. In another 1 km race, Bhuvan beats Chetan by 50 m. If all three run at their usual steady speeds, by how many metres would Aman beat Chetan in a 1 km race?

A dealer sells two phones for ₹9,900 each. On one he makes a profit of 10%, and on the other he makes a loss of 10%. What is his overall result on the two phones?

The cost price of 21 notebooks is equal to the selling price of 18 notebooks. What is the profit percentage?

Three friends try a puzzle independently. The chances that they solve it are $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$. What is the probability that the puzzle gets solved by at least one of them?

In how many ways can 7 people sit around a round table if two of them, Rahul and Sneha, must not sit next to each other?

Asha starts a business with ₹60,000. Four months later Bimal joins her with ₹80,000. At the end of the year the profit is ₹51,000, shared in the ratio of capital multiplied by time. What is Bimal's share?

To pass an exam a student needs 40% of the maximum marks. Riya scored 186 marks and failed by 34 marks. What are the maximum marks?

The table shows tourist arrivals, in thousands, at four hill stations.

Station: 2023, 2024

Shimla: 820, 902

Ooty: 560, 644

Munnar: 300, 357

Darjeeling: 480, 540

Which station had the highest percentage growth in arrivals from 2023 to 2024?

A delivery van's log for one trip has three legs.

Leg 1: 36 km in 45 minutes

Leg 2: 50 km in 1 hour 15 minutes

Leg 3: 24 km in 30 minutes

What was the van's average speed for the whole trip?

A line graph shows the total number of downloads of an app, in thousands, counted from launch, at the end of each month: January 12, February 30, March 45, April 70, May 88, June 120. What was the average number of new downloads per month from February to June?

The table shows four hotels' rooms, average occupancy and room rate on a typical night.

Hotel: rooms, occupancy, rate per room

Bayview: 120, 75%, ₹5,000

Hilltop: 80, 90%, ₹6,000

Lakeside: 150, 64%, ₹4,000

City Inn: 100, 84%, ₹5,500

Which hotel earns the most room revenue on a typical night?

A bar chart shows the number of startups funded in a city, by sector.

Year: 2022, 2023, 2024

Fintech: 50, 35, 45

Edtech: 30, 18, 12

Health: 20, 27, 33

By how many percentage points did health's share of all funded startups change from 2022 to 2024?

A share was priced at ₹500 at the start of a year. The table gives its percentage change in each of the next four months, each change applied to the price at the end of the month before.

January: +10%

February: -20%

March: +25%

April: -10%

What was the share's price at the end of April?

A bar chart shows a juice bar's total sales, in ₹ thousand, in four months of a leap year: February (29 days) 300, March (31 days) 310, April (30 days) 306, May (31 days) 315. In which month were the average daily sales the highest?

Introducing a man, Sunita says, "He is the son of the only brother of my husband's mother." How is the man related to Sunita?

Gita's father-in-law is Hemant. Hemant has only one child, his son Ishan. Ishan's daughter is Jiya. How is Gita related to Jiya?

Eight people sit in two parallel rows of four that run from west to east. Ankit, Bela, Chetna and Dhruv sit in Row 1, facing south. Pari, Raunak, Sana and Tejas sit in Row 2, facing north, so each person directly faces one person in the other row. Left and right are taken from each person's own point of view. Bela sits at one end of Row 1 and faces Sana. Ankit sits second to the right of Bela. Tejas faces Dhruv. Raunak sits immediately to the left of Sana. Who faces Ankit?

Five friends, Ishita, Jay, Kriti, Lakshay and Mehak, all scored different marks in a test. Ishita scored 12 marks more than Jay. Kriti scored 5 marks less than Ishita. Lakshay scored more than Kriti but less than Ishita. Mehak scored less than Jay. Who scored the third-highest marks?

A delivery robot starts facing east and moves 15 m. It turns left and moves 4 m, turns left again and moves 3 m, then turns right and moves 1 m before stopping. How far is it from its starting point, and in which direction?

Six boxes, labelled P, Q, R, S, T and U, are stacked one on top of another in a single pile. Box S is at the bottom. Exactly two boxes are between box R and box U. Box Q is directly on top of box R. Box P is directly below box T. Which box is third from the top?