Masters' Union MUSAT · Paper 10

A train usually covers its route at 60 km/h. One day it runs at 50 km/h throughout and arrives 24 minutes late. How long is the route?

A shop sold a lamp at a profit of 7%. Had it sold the lamp for ₹45 more, its profit would have been 12%. What was the cost price of the lamp?

A class committee has 5 boys and 4 girls. Two members are picked at random to represent the class. What is the probability that both are girls?

Six friends, including Ira and Jai, sit in a row of six seats in a random order. What is the probability that Ira and Jai take the two end seats?

There are 10 points in a plane. Exactly 4 of them lie on one straight line, and no other three of the points lie on a straight line. How many triangles can be drawn with their corners at these points?

A locker code is made of two different letters of the English alphabet followed by two digits from 0 to 9. The two digits may be the same, and the order of every character matters. How many such codes are possible?

A sum of money invested at compound interest, compounded yearly, grows to ₹13,310 in 3 years and to ₹14,641 in 4 years. What was the sum invested?

A grouped bar chart shows smartphone shipments, in millions, by brand in a market.

Brand: 2023, 2024

Astra: 12, 13

Bolt: 9, 12

Crest: 6, 6

Others: 13, 19

How did Bolt's share of total shipments change from 2023 to 2024?

The table shows a spice exporter's pepper production and the share of its exports that went to Dubai.

Year: 2022, 2023, 2024

Production (tonnes): 40, 45, 50

Dubai's share of exports: 50%, 45%, 40%

Every year the exporter exports between 20% and 30% (both included) of its production, and sells the rest within India. In 2024, what is the greatest possible quantity exported to places other than Dubai, as a percentage of the quantity sold within India?

A bar chart shows how many students of a college were placed through campus drives and through off-campus offers.

2021: campus 120, off-campus 80

2022: campus 150, off-campus 90

2023: campus 140, off-campus 110

2024: campus 180, off-campus 120

In which year was the campus share of all placements the highest?

A bar chart shows a hostel's monthly electricity use, in units.

Jan 4,200; Feb 3,900; Mar 4,500; Apr 5,200; May 6,100; Jun 6,400

Each month is billed on its own: the first 4,000 units at ₹6 per unit and every unit above 4,000 at ₹8 per unit. What was the total bill for the three months with the highest use?

A line graph shows a new café's monthly revenue and expenses, in ₹ thousand, for its first six months.

January: revenue 80, expenses 120

February: revenue 95, expenses 120

March: revenue 110, expenses 115

April: revenue 130, expenses 118

May: revenue 145, expenses 120

June: revenue 160, expenses 125

At the end of which month did the café's total profit since opening first become positive?

The table gives a family's monthly spending in 2020 on three items, and each item's 2024 price index (2020 = 100).

Rice: ₹1,200, index 135

Cooking oil: ₹800, index 160

Milk: ₹2,000, index 128

If the family buys the same quantities in 2024, by what percentage has its monthly spending on these three items risen since 2020?

The table shows how 50 students scored in a test marked out of 100 (marks are whole numbers).

0 to 20: 4 students

21 to 40: 9 students

41 to 60: 15 students

61 to 80: 14 students

81 to 100: 8 students

What is the least possible number of students who scored more than 50?

Dhruv's sister Isha is married to Karan. Karan's father, Prakash, has only two children: Karan and a daughter, Lekha. Lekha's son is Varun. How is Varun related to Isha?

Six friends, Uday, Vani, Wasim, Xena, Yuvraj and Zoya, sit in a row, all facing south. Left and right are taken from the friends' own point of view, so each person's right is towards the west. Wasim sits at the extreme right end of the row. Zoya sits second to the left of Wasim. Xena sits immediately to the left of Zoya. Uday sits immediately to the left of Yuvraj. Who sits immediately to the right of Zoya?

Sameer walks 10 m south, turns left and walks 6 m, turns left again and walks 18 m, then turns right and walks 9 m. How far is he from his starting point, and in which direction?

Two cyclists start from the same crossing. Aditi rides 12 km east and then 5 km north. Bhanu rides 4 km west and then 7 km south. How far apart are they now, and in which direction is Aditi from Bhanu?

Pihu, Rohan, Sara and Tarun each bought a different juice (mango, orange, apple or guava) at a different price (₹40, ₹50, ₹60 or ₹70). The mango juice cost ₹70 and the orange juice cost ₹40. Pihu bought the guava juice. The apple juice cost more than the guava juice. Sara paid ₹10 more than Rohan. Which juice did Sara buy?

A three-storey building has two flats on each floor, one on the west side and one on the east side, with floor 1 at the bottom. Six friends, Amrit, Bhavya, Charan, Disha, Eknoor and Faisal, live one in each flat. Disha lives in the east flat on floor 2. Amrit lives directly above Charan, in the flat on the same side one floor up. Eknoor lives in a west-side flat, on a higher floor than Bhavya. Who lives on the same floor as Eknoor?