Deloitte Aptitude Questions

1. The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 275, then the mean profit for the last 15 days would be
   1. Rs. 200
   2. Rs. 350
   3. Rs. 275
   4. Rs. 425
   Answer & Explanation
   Answer: Option D
   Average would be : 350 = (275 + x)/2
   On solving, x = 425.

2. There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day while the average expenditure per head diminishes by Re 1. Find the original expenditure of the mess.
   1. Rs. 480
   2. Rs. 520
   3. Rs. 420
   4. Rs. 460
   Answer & Explanation
   Answer: Option C
   Let d be the average daily expenditure
   Original expenditure = 35 × d
   New expenditure = 35 × d + 42
   New average expenditure will be :
   (35 × d + 42)/42 = d - 1
   On solving, we get d = 12
   Therefore original expenditure = 35 × 12 = 420
3. The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day Rs. 1,325 were collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?
   1. Rs. 750
   2. Rs. 1000
   3. Rs. 850
   4. Rs. 1250
   Answer & Explanation
   Answer: Option D
   Let x be the number of passengers and y be the fare taken from passengers.
   3xy + 50xy = 1325 => xy = 25
   Amount collected from II class passengers = 25 × 50 = Rs. 1250.

4. A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9 km/hour and the speed of the current is 3 km/hour, the distance between A and B is
   1. 4 km
   2. 8 km
   3. 6 km
   4. 12 km
   Answer & Explanation
   Answer: Option D
   Let d be the distance between A and B
   So, d/12 + d/6 = 3 d = 12 km
5. A man while returning from his factory, travels 2/3 of the distance by bus, ¾ of the rest partly by car and partly by foot. If he travels 2 km on foot, find the distance covered by him.
   1. 24 km
   2. 22 km
   3. 28 km
   4. 26 km
   Answer & Explanation
   Answer: Option A
   [image]
   Therefore D = 24 km

6. The fuel indicator in a car shows 1/5th of the fuel tank as full. When 22 more liters of fuel are poured in to the tank, the indicator rests at the 3/4of the full mark. Find the capacity of the tank.
   1. 25 litres
   2. 35 litres
   3. 30 litres
   4. 40 litres
   Answer & Explanation
   Answer: Option D
   x/5 + 22 = 3x/4 ⇒ x = 40 litres
7. A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 m³. The emptying capacity of the pump is 10m³ per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump.
   1. 45 m³/min
   2. 40 m³/min
   3. 50 m³/min
   4. 55 m³/min
   Answer & Explanation
   Answer: Option C
   (2400/x) - (2400/(x + 10)) = 8, Solving this we get x
   = 50m³/min
   Or by options (2400/50) - (2400/60) = 48 - 40 = 8 minutes
8. A sum of money is accumulating at compound interest at a certain rate of interest. It simple interest instead of compound were reckoned, the interest for the first two years would be diminished by Rs. 20 and that for the first three years, by Rs 61. Find the sum
   1. Rs. 7000
   2. Rs. 8000
   3. Rs. 7500
   4. Rs. 6500
   Answer & Explanation
   Answer: Option B
   [image]
9. In a kilometer race, A can give B a 100 m start and C a 150 m start. How many meters start can B give to C?
   1. 50
   2. 50/9
   3. 8500/9
   4. 500/9
   5. None of these
   Answer & Explanation
   Answer: Option D
   A can give B a 100 m start and C a 150m. Start means when A runs 1000m, B runs 900m and C runs 850m. When B runs 1000m, C will run 1000 x (850/900) m (i.e. 8500/9 m) Thus, B can give C a start of - 1000 - (8500/9), i.e. 500/9 m.
10. The average age of all the student of a class is 18 years. The average age of boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.
    1. 15
    2. 45
    3. 30
    4. 50
    Answer & Explanation
    Answer: Option C
    Let Boys in class = B
    Girls in class = 20
    Now, (20B+15*20)/(B+20) = 18
    ⇒ B = 30