# RS Aggarwal Quantitative Aptitude PDF Free download: AVERAGE

**6.AVERAGE**

**Ex.1:Find the average of all prime numbers between 30 and 50?**

**Sol:** there are five prime numbers between 30 and 50.

They are 31,37,41,43 and 47.

Therefore the required average=(31+37+41+43+47)/5 ó199/5 ó 39.8.

**Ex.2. find the average of first 40 natural numbers?**

**Sol:** sum of first n natural numbers=n(n+1)/2;

So,sum of 40 natural numbers=(40*41)/2 ó820.

Therefore the required average=(820/40) ó20.5.

**Ex.3. find the average of first 20 multiples of 7?**

**Sol:** Required average =7(1+2+3+…….+20)/20 ó(7*20*21)/(20*2) ó(147/2)=73.5.

**Ex.4. the average of four consecutive even numbers is 27. find the largest of these** **numbers?**

**Sol:** let the numbers be x,x+2,x+4 andx+6. then,

(x+(x+2)+(x+4)+(x+6))/4) = 27

ó(4x+12)/4 = 27

óx+3=27 ó x=24.

Therefore the largest number=(x+6)=24+6=30.

Ex.5. there are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?

**Sol:** total weight of(36+44) students=(36*40+44*35)kg =2980kg.

Therefore weight of the total class=(2980/80)kg =37.25kg.

Ex:6.nine persons went to a hotel for taking their meals 8 of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine.What was the total money spent by them?

**Sol:** Let the average expenditure of all nine be Rs.x

Then 12*8+(x+8)=9x or 8x=104 or x=13.

Total money spent = 9x=Rs.(9*13)=Rs.117.

Ex.7: Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number.

**Sol**: Let the third number be x.

Then second number = 3x.

First number=3x/2.

Therefore x+3x+(3x/2)=(44*3) or x=24

So largest number= 2^{nd} number=3x=72.

**Ex.8:The average of 25 result is 18.The average of 1 ^{st} 12 of them is 14 & that of last 12 is 17.Find the 13^{th} result.**

**Sol**: Clearly 13^{th} result=(sum of 25 results)-(sum of 24 results)

=(18*25)-(14*12)+(17*12)

=450-(168+204)

=450-372

=78.

**Ex.9:The Average of 11 results is 16, if the average of the 1 ^{st} 6 results is 58 & that of the last 63. Find the 6^{th} result.**

**Sol**: 6^{th} result = (58*6+63*6-60*11)=66

Ex.10:The average waight of A,B,C is 45 Kg. The avg wgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.

**Sol. **Let A,B,c represent their individual wgts.

Then,

A+B+C=(45*3)Kg=135Kg

A+B=(40*2)Kg=80Kg & B+C=(43*2)Kg=86Kg

B=(A+B)+(B+C)-(A+B+C)

=(80+86-135)Kg

=31Kg.

Ex. 11. The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.

**Sol.** Total age of 39 persons = (39 x 15) years

= 585 years.

Average age of 40 persons= 15 yrs 3 months

= 61/4 years.

Total age of 40 persons = __(_(61/4 )__x 40) years= 610 years.

:. Age of the teacher = (610 – 585) years=25 years.

**Ex. 12. The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53 kg is replaced by a new man. Find the weight of the new**

** man.**

**Sol.** Total weight increased =(1.8 x 10) kg =18 kg.

:. Weight of the new man =(53 + 18) kg =71 kg.

**Ex. 13. There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess?**

**Sol.** Let the original average expenditure be Rs. x. Then,

42 (x – 1) – *35x=*42 ó* 7x= *84 ó x =12.

Original expenditure = Rs. (35 x 12) =Rs. 420. .

**A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning.**

**Sol.** Let the average after 17th inning = x.

Then, average after 16th inning = *(x *– 3).

:. 16 (x – 3) + 87 = *17x *or *x *= (87 – 48) = 39.

**Ex.15. Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km perhour. Find the average speed of the train during the whole journey.**

**Sol.** Required average speed = ((2xy)/(x+y)) km / hr

=(2 x 84 x 56)/(84+56)km/hr

= (2*84*56)/140 km/hr

=67.2 km/hr.