Masters' Union MUSAT · Paper 6

A delivery rider covers the first half of a 60 km route at 40 km/h and the second half at 60 km/h. What is her average speed for the whole route?

A 240 m long goods train runs at 36 km/h. An express train 160 m long runs at 72 km/h in the same direction on a parallel track. How long does the express take to overtake the goods train completely?

A grocer mixes 40 kg of rice bought at ₹45 per kg with 60 kg bought at ₹50 per kg, and sells the whole mixture at ₹57.60 per kg. What is his profit percentage?

A bag holds 4 red, 5 green and 3 blue marbles. Three marbles are drawn at random, all at once. What is the probability that they are all of different colours?

How many 4-digit numbers divisible by 5 can be formed from the digits 0, 1, 2, 3, 4 and 5 if no digit is repeated?

The price of cooking oil rises by 25%, and a family cuts the quantity of oil it buys by 16%. By what percentage does the family's spending on oil change?

Asha and Bilal together can paint a hall in 12 days, Bilal and Chirag together in 15 days, and Asha and Chirag together in 20 days. How many days would Asha take to paint the hall alone?

The table shows orders, in thousands, placed on a food-delivery app in three cities.

City: April, May, June

Pune: 42, 48, 55

Jaipur: 30, 36, 39

Kochi: 18, 21, 26

In May, what percentage of the three cities' total orders came from Jaipur, correct to one decimal place?

A bar chart shows the yearly revenue of a bike-rental company, in ₹ crore: 2020: 20, 2021: 27, 2022: 34, 2023: 41, 2024: 50. In which year was the percentage growth in revenue over the year before the highest?

The table shows how a family's monthly income of ₹96,000 is split.

Rent 25%, Food 20%, Education 15%, Transport 10%, Others 12%, Savings: the rest

Next month the rent goes up by ₹2,400. The income stays the same, and the extra rent comes entirely out of savings. What percentage of the income will then be saved?

A line graph shows the monthly sales, in units, of two phone models.

Model P: Jan 120, Feb 135, Mar 150, Apr 165, May 180

Model Q: Jan 90, Feb 110, Mar 120, Apr 140, May 165

Over these five months, the average monthly sales of Model P were how many times the average monthly sales of Model Q?

The table shows how many students appeared and how many passed at four coaching centres.

Alpha: 2023, 260 passed of 400; 2024, 336 passed of 480

Beta: 2023, 210 passed of 300; 2024, 243 passed of 360

Gamma: 2023, 150 passed of 250; 2024, 216 passed of 320

Delta: 2023, 300 passed of 500; 2024, 352 passed of 550

Which centre's pass percentage rose by the most percentage points from 2023 to 2024?

In a survey of 2,400 shoppers on how they prefer to pay, 15% chose cash. The table splits all the other replies.

Mode: share of the non-cash replies

UPI: 60%

Card: 25%

Wallet: 15%

How many shoppers chose card?

A bar chart shows the monthly output, in tonnes, of two factories.

Factory X: Jan 96, Feb 110, Mar 99, Apr 130, May 126, Jun 90

Factory Y: Jan 80, Feb 88, Mar 85, Apr 104, May 100, Jun 78

In how many of these months was Factory X's output more than 120% of Factory Y's output?

Harish and his wife Pallavi have two children, a daughter Lata and a son Mohit. Mohit is married to Nisha, and they have a daughter, Riya. Lata is married to Sameer, and they have a son, Om. How is Nisha related to Om?

Seven friends, Kunal, Lavanya, Manish, Naina, Omkar, Prisha and Rehan, sit in a row, all facing north, so each person's right is towards the east end. Naina sits third from the right end. Exactly two people sit between Naina and Kunal. Omkar sits immediately to the right of Kunal. Prisha sits at one of the two ends. Rehan does not sit next to Naina. Lavanya sits somewhere to the left of Manish, and Rehan sits somewhere to the left of Prisha. Who sits second from the right end?

In a row of students, Vivek is 14th from the left end and Simran is 17th from the right end. When the two of them swap places, Vivek becomes 25th from the left end. How many students are in the row?

Starting from her home, Tanvi drives 4 km north, turns right and drives 6 km, turns right again and drives 16 km, then turns left and drives 3 km to reach her office. Standing at her office, how far away is her home, and in which direction from the office does it lie?

Ishaan, Jaya, Karan and Leela each bought a different gadget (a laptop, a phone, a tablet or a watch), each on a different day from Monday to Thursday. The tablet was bought on Wednesday and the laptop on Thursday. Jaya bought her gadget the day after Karan bought his. Leela bought the watch, but not on Monday. Who bought the phone?

Six people, Anil, Bela, Chand, Dina, Eshan and Fiza, live on the six floors of a building, one on each floor, with floor 1 at the bottom and floor 6 at the top. Dina lives on an even-numbered floor, and Chand lives on the floor immediately above Dina. Exactly two people live between Anil and Chand. Fiza lives on the floor immediately above Anil. Bela lives on some floor above Anil. Who lives on the floor immediately below Dina?