Average Problems – SBI PO Prelims 2015



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1. Ten years ago, the
average age of a family of 4 members was 24 years. Two children having been
born, the average age of the family is
same today. What is the present age of the youngest child if they differ in age by 2 years?
(a) 1 year
(b) 2 years
(c) 3 years
(d) 5 years
(e) None of these
2. The average of 8
readings is 24.3, out of which the average of first two is 18.6 and that of
next three is 21.2. If the sixth
reading is 3 less than seventh and 8 less than eighth, what is the sixth
reading?
(a) 24.8
(b) 26.5
(c) 27.6
(d) 29.4
(e) None of these
3. The average age of
11 players of a cricket team is decreased by 2 months when two of them aged 17
years and 20 years are replaced by two
reserve players. The average age of the players is
(a) 18 years 3 months
(b) 17 years 1 month
(c) 17 years 7 months
(d) 17 years 11 months
(e) None of these
4. Average marks obtained
by 120 candidates was 35. If the average marks of passed candidates was 39 and that of failed candidates was 15 the
number of candidates who passed the examination is
(a) 100
(b) 80
(c) 95
(d) 105
(e) None of these
5. A cyclist rides 24
km at 16 km per hour and a further 36 km at 15 km per hour. Find his average
speed for the journey.
(a) 15·38 km per hour
(b) 16 km per hour
(c) 15·5 km per hour
(d) 16.38 km per hour
(e) None of these
6. A certain factory
employed 600 men and 400 women and the average wage was Rs. 2·55 per day. If a
woman got 50 p. less than a man, what were
their daily wages ?
(a) Man Rs. 2·75, woman Rs. 2·25
(b) Man Rs. 3·25, woman Rs. 2·75
(c) Man Rs. 3, woman Rs. 2·50
(d) Man Rs. 2·50 woman Rs. 2
(e) None of these
7. If a train maintains
an average speed of 40 km an hour it arrives at its destination punctually. if
however the average speed is 35 kn an
hour it arrives 15 minutes late. Find the length of  the journey in km.
(a) 40
(b) 70
(c) 30
(d) 80
(e) None of these
8. The average weight
of three men A, B, C is 84 km and fourth man D joins them the average weight of
the four becomes 80 km. If E whose wt. is
3 kg more than D replaces A, then the average wt. of B, C, D and E becomes 79 kg. Find the weight of A.
(a) 75 kg
(b) 80 kg
(c) 70 kg
(d) 85 kg
(e) None of these
9. A man walks from P
to Q at the rate of 5 km an hour and returns from Q to P at the rate of 3 km an
hour. What is the average rate in km per
hour for the whole journey ?
(a) 4
(b) 15/4
(c) 1/4
(d) 9/2
(e) None of these
10. A ship 40 km from
shore springs a leak which admits 3 3/4 quintals of water
in 12 minutes. 60 quintals would suffice
to sink the ship, But its pump can throw out 12 quintals of water in one hour.
Find the average rate of sailing so that
it may reach the shore just it begins to sink.
(a) 4 km/h
(b) 4·5 km/h
(c) 5 km/h
(d) 6 km/h
(e) None of these




Solutions::


1. Ten years ago average of four members was 24 years. Presently
average age of six members is 24. Let the present age of eldest and youngest
child is x and y respectively
136+x+y/6 = 24
or x + y = 8 …(i)
Q
x – y = 2 …(ii)
On solving, x = 5 years and y = 3 years
So, Youngest child is of 3 years.
2.  Let 6th reading be
x, then 7th reading = x + 3, 8th
reading = x + 8
So, we have
18.6 * 2 + 21.2 * 3 + x + x +3 +x +8/8 = 24.3
3x + 37.2 + 63.6 + 11 = 24.3 × 8
3x + 111.8 = 194.4
3x = 82.6
x = 27.53
i.e. 27.6 approximately
3. Let x be the average age of 11 players, and y be the
average of the reserve players
(11x + 2y – 17 – 20)/11 = x – 2/12 or y = 211/12
So, 17 years 7 months
4. Let the number of students who passed be x and number of
students who failed is 120 –x
x × 39 + (120 – x) × 15 = 120 × 35
x = 100
5. Time taken to travel 24 km with the speed of 16 km/hour.
= 24/16 = 3/2 hour.
Similarly time taken to travel 36 km with the speed of 15
km/hour. = 36/15 = 12/5 hour.
Total distance travelled = 36 + 24 = 60 km
and total time taken to travel distance
= 3/2 + 12/5 hour
= 39/10 hour
Hence average speed = 60 × 10/39
= 200/13
= 15·38
6. Total workers = 600 + 400 = 1,000
Total wages per day = 2·55 × 1‚000
= Rs. 2‚550.
Since a man gets 50 P. more, 600 men will get Rs. 600 × ·50
= Rs. 300 more.
∴ 2,550 – 300 =
2,250 is the daily wages of 1,000 women.
Hence, daily wage of man is
= 2·25 + ·50
= Rs. 2·75
and daily wage of women
= Rs. 2·25
7. L.C.M. of 40 and 35 = 280.
Let the journey be 280 km
If the speed is 40 km/hour, time taken = 280
40 = 7 hrs.
If the speed is 35 km/hour, time taken = 280
35 = 8 hrs.
Difference of times
= 8 – 7 = 1 hour
= 60 minutes
If 60 minutes is the difference, length of journey = 280 km
If 15 minutes is the difference, journey
= 280/60 × 15 = 70 km
8.  Sum of wt. of
A, B and C = 84 × 3 = 252 kg
Sum of wt. of
A, B, C and D = 80 × 4 = 320 kg
wt. of D = 320 – 252 = 68 kg
wt. of E = 68 + 3 = 71 kg
Sum of wt. of
B, C, D, E = 79 × 4 = 316 kg
wt. of (B + C) = 316 – 68 – 71
= 177 kg
wt. of A = 252 – 177
= 75 kg
9.  Let the length of
journey be L.C.M. of 3, 5 = 15 km
Time taken in going P to Q = 15/5 = 3 hr
Time taken in coming Q to P = 15/3 = 5 hr
Total time in going and coming back
= 5 + 3 = 8 hr
Hence, the average speed
= 30/8 =15/4 km/hr
10. In 12 minutes leak admits
= 15/4 quintals
One hour leak admits
= 15/4 × 60/12 = 75/4 quintals
In one hour pumps throw out
= 12 quintals
Water left in the ship in one hour
= 75/4  – 12
= 27/4 quintals
∴ 27/ 4 quintals of water is left in the ship in
 = 1 hour.
⇒ 60 quintals of water is left in = 1 × 60 × 4/27 = 80/9 hour
Now in 80/9 hour the ship runs = 40 km
1 hour the ship runs = 40 × 9/80
= 4·5 km

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