The average age of n persons is 55.Two persons aged 41 and 47 respectively leave the group and three new persons aged between 60 and 65 join the group. If the average age of the group goes up by one year and if the initial number of people in the group is a multiple of 7, what is the number of persons now in the group?
The average age of n persons is 55.Two persons aged 41 and 47 respectively leave the group and three new persons aged between 60 and 65 join the group. If the average age of the group goes up by one year and if the initial number of people in the group is a multiple of 7, what is the number of persons now in the group?
The correct option is B 43
Let x,y,x be the ages of 3 persons which lies between 60 and 65
The equation governing the problem 55n−41−47+(x+y+z)n+1=56
Also given n is a multiple of 7
55n - 88 +k = 56n + 56 where k=x+y+z, n+ 144=k
Now k ranges between 3 × 61 and 3× 64
183 ≤ n+44 ≤ 192
39 ≤ n ≤ 48
Thus n =42, the latest number n + 1 =42+1=43
Shortcut
Go from answer options. The initial number of people in the group is a multiple of 7. The answer options give the number of initial people + 1. Thus the correct answer is option (b).
43
Let x,y,x be the ages of 3 persons which lies between 60 and 65
The equation governing the problem 55n−41−47+(x+y+z)n+1=56
Also given n is a multiple of 7
55n - 88 +k = 56n + 56 where k=x+y+z, n+ 144=k
Now k ranges between 3 × 61 and 3× 64
183 ≤ n+44 ≤ 192
39 ≤ n ≤ 48
Thus n =42, the latest number n + 1 =42+1=43
Shortcut
Go from answer options. The initial number of people in the group is a multiple of 7. The answer options give the number of initial people + 1. Thus the correct answer is option (b).
