Different Competition : Solved Problem

Q1. The average age of 26 students in a class is 26 years. If the age of the teacher is also included, the average age of the whole group becomes 27 years. Find the age of the teacher.


Options: A. 53 | B. 50 | C. 57 | D. 54


Soln



  • Total age of 26 students = 26 × 26 = 676

  • Total persons including teacher = 26 + 1 = 27

  • Total age including teacher = 27 × 27 = 729

  • Teacher's age = 729 − 676 = 53 years


Ans: A. 53 years


Q2. Smriti travels to a shopping mall at a speed of 21 km/hr and returns at a speed of 69 km/hr. Find her average speed for the entire journey.


Options: A. 30.3 km/hr | B. 40.2 km/hr | C. 23.4 km/hr | D. 32.2 km/hr


Soln


For equal distances,


Average Speed = 2xy / x+y


Here, x = 21 km/hr, y = 69 km/hr


Average Speed = 2 × 21 × 69 / 21 + 69 = 2898 / 90


Ans: D. 32.2 km/hr


Shortcut: Average Speed = 2xy / x+y ​​(Used when the distances are equal.)


Q) 0.4 + 0.44 + 0.444 + 0.4444 + 0.44444 = ?


Trick: Take the highest number of digits: 0.44444 → 5 digits


Write backward counting: 54321


Multiply by the repeating digit 4: 54321 × 4 = 217284 


Now put the decimal point according to the biggest number (5 digits after decimal): 2.17284


Ans = 2.17284 (B)


Q) 4 + 44 + 444 + 4444 + 44444



  1. Highest number has 5 digits → write 12345

  2. Multiply by the repeated digit 4


               12345 × 4 = 49380


Ans = 49380


Trick:  For: a + aa + aaa + aaaa + aaaaaa


Use: 12345 × a


(where 12345 has the same number of digits as the largest repeated number).