averages Model Questions & Answers, Practice Test for ssc mts paper 1
The average earning of a group of persons is Rs. 50 per day. The difference between the highest earning and lowest earning of any two persons of the group is Rs. 45. If these two people are excluded the average earning of the group decreased by Rs. 1. If the minimum earning of the person in the group lies between 42 and 47 and the number of persons initially in the group was equal to a prime number, with both its digits prime. The number of persons in the group initially was:
Answer: (d)
Let there be n people (initially) in the group, then the total earning of the group = n × 50
Again n × 50 = (n – 2) × 49 + (2x + 45)
⇒ n = 2x – 53; where x is the lowest earning of any person.
Now, since 42 < x < 47 and n Î prime numbers
Then the only possible value of n = 37 for x = 45.
The average weight of 45 students in a class was calculated as 36 kgs. It was later found that the weight of two students in the class was wrongly mentioned. The actual weight of one of the boys in the class was 32 kgs. but it was mentioned as 34 kgs and the weight of another boy in the class was 45 kgs. whereas it was mentioned as 40 kgs. What is the actual average weight of the 45 students in the class? (Rounded off to two-digits after decimal)
Answer: (b)
Actual average weight
= $36 + (32 + 45 - 34 - 40)/45$
= 36 + $3/45$
= 36 + 0.07 = 36.07 kgs.
A person divides his total route of journey into three equal parts and decides to travel the three parts with speeds of 40, 30 and 15 km/hr respectively. Find his average speed during the whole journey.
Answer: (c)
By the theorem: Average speed
= ${3 × 40 × 30 × 15}/{40 × 30 + 30 × 15 + 40 × 15}$
= ${3 × 40 × 30 × 15}/2250$ = 24 km/hr
The respective ratio between the speeds of a car, a train and a bus is 5 : 9 : 4. The average speed of the car, the bus and the train is 72 km/h together. What is the average speed of the car and the train together ?
Answer: (c)
Total speed of car, bus and train
= 72 × 3 = 216 km
Speed of car and train
= ${5 + 9}/{5 + 9 + 4} × 216$ = 168 km
Average = $168/2$ = 84km
How much tea at Rs. 9 per kg must be mixed with 100 kg of superior tea at Rs. 13.50 per kg to give an average price of Rs. 11 per kg?
Answer: (b)
Let x kg of tea of Rs. 9 per kg.
${9 × x × 13.5 × 100}/{x + 100}$ = 11
⇒ 9x + 1350 = 11x + 1100
⇒ 2x = 250
∴ x = 125 kg.
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