Quantative Aptitude Question for SBI PO,DMRC,NMRC,IBPS,BANK,SSC

*************Question on Average************

1).The average age of a group of 20 boys is increased by one year when 5 of them whose average age was 20 years are replaced by 5 new boys. The average age of new comers is ?

Solution: 

Let 'x' be the sum of ages of first 20 boys.

Let 'y' be the sum of ages of 5 old boys and

'z' be the sum of ages of 5 new boys. 

Given : y/5 = 20 or y = 100 

(x - y + z) / 20 = 1 + (x/20) 

(x-100 +z)/20 = (x/20) + 1 

or z/20 = 6 or Z = 120

Average of 5 new comers = Z / 5 = 120 / 5 = 24 years

2).

Nine man went to a hotel. Eight of them spent rs 10 each on their meals. The ninth man spent rs 4 more than the average of all of them. How much did the ninth man spend?

The first eight men spent rs 80 and the ninth man spent rs x. 
The sum that all 9 men spent was 80+x


The average of all nine men was rs 

The equation comes from this sentence:

The ninth man spent rs 4 more than the average of all of them.

.

Clear of fractions by multiplying through by 9:









Solution: rs 14.50

Average =  = 

The ninth man spent rs 14.5 and the others spent rs 10.  So

he spent rs 4 more than what the others spent.

3). If the average of m numbers is y, and when x is added to the m numbers, the average of the m+1 numbers is b, then x is equal to which of the following.Please show me the steps.

lets assume the sum of the m numbers = A
so A/m=y so A=my

when x is added to the m numbers the total sum of these number will be A+x and the number of these numbers will be m+1
so (my+x)/m+1 = b
my+x= bm+b

x= b(m+1)-my

4).The monthly salary of a person was Rs 320 for each of the first 3 years. He next got annual increment of Rs 40 per month for each of the following successive 12 years.His salary remained stationary till retirement when he found that his average monthly salary during his service period was Rs 694. Find the period of his service?

Let the number of year in service is:x

first 2 year he has salary of=320*2*12=7680
He gets salary in AP start from 3 year

320*12,(320+40)*12,(360+40)*12...............
3840,4320,4800,.......uptp 13 term
first term a=3840,
difference d=480,

Salary per year after increment t13=3840+(13-1)*480=9600
no  of term =12+1=13,
Sn=n/2[2a+(n-1)*d]
Sn=13/2(2*3840+(13-1)*480)=87360

x=40years
2*3840+87360+(x-(13+2))*9600/12x=698









5) .The average weight of 3 Men A, B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. 

If another man E whose weight is 3 kg more than that of D, replaces A, then the average weight of B, C, D and E becomes 79 kg.

Then weight of A is:

The average weight of A,B and C = 84Kg
The total weight of A, B and C = 84 x 3 = 252Kg.
The average weight of A, B , C and D = 80 kg
The total weight of A, B, C and D = 80 x 4 = 320 kg
The weight of D = 320 – 252 = 68 kg
The weight of Q = 68 + 3 = 71 kg
The average weight of B, C ,D and E = 79 kg
The total weight of B, C, D and E = 79 x 4 = 316 kg
The total weight of A,B, C and D  – the total weight of B,C,D and E = 320 – 316 = 4 kg
A – E = 4
A = 4 + E
A = 4 + 71
A = 75 Kg

6).The average age of a committee of seven trustees is the same as it was five years ago, a younger man having been substituted for one of them. How much younger was he than the trustee whose place he took?

Lets assume that the sum of the age of the unchanged trustees 5 years ago be x. Also the age of the replaced trustee and the new trustee, five years ago be y and z respectively.

Thus we get y - z = 35

Now since the average age of the current committee and the previous committee is same,

(x + y)/7=(x + z + 35)/7

Therefore the age gap is 35.

The 35 value accounts for the time lapse of 5 years for each of the 7 trustees.