Quant Questions – Average Problems with Solution Set 7

Dear Readers, Important Average Problems for upcoming competitive Exams with Solutions. Average is an important topic from banking exam point of view. You could solve Average problems easily if you understand the basic concepts. Aspirants preparing for SBI Clerk, SBI PO, IBPS Clerk, IBPS PO, Insurance, RBI and other competitive examination can make of use these average problems. We have included some important average problems that are repeatedly asking in competitive exams. Practice lot of questions to become an expert in solving average problems and learn to use shortcuts.

Average Problems – Set 7

1).From a tank containing 100L of guava juice, 10L are drawn out and an equal amount of water is added. From the mixture, 10L is again drawn out and same quantity of water is added. What is the final ratio of guava juice to water?
a) 90:10
b) 91:9
c) 81:19
d) 80:20
e) None of the above
2).A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit?
a) 2000
b) 2500
c) 2660
d) 2700
e) None of these
3).In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
a) 7600
b) 8020
c) 8400
d) Data Inadequate
e) None of the above
4).10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was
a) 25020
b) 33000
c) 35000
d) 40000
e) None of the above
5).8% of the people eligible to vote are between 18 and 21 years of age. In an election, 85% of those eligible to vote, who were between 18 and 21, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote?
a) 4.2
b) 6.4
c) 6.8
d) 8
e) None of the above
6).Pragya spends 24% of her monthly income on food and 15% on the education of her children. Of the remaining salary, she spends 25% on entertainment and 20% on conveyance. She is now left with Rs. 10,736. What is the monthly salary of Pragya?
a) Rs. 27,600
b) Rs. 28,000
c) Rs. 31,200
d) Rs. 33,000
e) None of the above
7).A shopkeeper gives 3 consecutive discounts of 10%, 15% and 15% after which he sells his goods at a percentage profit of 30.05% on the cost price. Find the value of  the percentage profit that the shopkeeper would have earned if he had given discounts of 10% and 15% only:
a) 53%
b) 62.5%
c) 72.5%
d) 68.6%
e) None of these
8).Two planes move along a circle of circumference 1.2 kms with constant speeds. When they move in different directions, they meet every 15 seconds and when they move in the same direction one plane overtakes the other every 60 seconds. Find the speed of the slower plane:
a) 0.04 km/s
b) 0.03 km/s
c) 0.05 km/s
d) 0.02 km/s
e) None of these
9).The metro service has a train going from Mumbai to Pune and Pune to Mumbai every hour. The first one at 6 a.m. The trip from one city to another takes 4.5 hours,  and all trains travel at the same speed. How many trains will pass while going from Mumbai to Pune, if you start at 12 noon?
a) 8
b) 10
c) 13
d) 9
e) None of these
10).A bus left Delhi for Ambala at 50 km/hr and turned over the same route at 40 km/hr. Thus it took 1 hour more on the return trip. The distance between Delhi and  Ambala is:
a) 200 kms
b) 180 kms
c) 400 kms
d) 300 kms
e) None of these
1)c   2)c   3)e   4)e   5)c   6)e   7)a   8)c  9)d   10)a  
1. C)Here, a=10L, n=2, x=100L
Quantity of guava juice in end =x (1-a/x)^n =100 * (1-10/100)^2 =81 L
Required ratio =81:(100-81)=81:19
2. C)Remain profit  for A, B& C = 7400 * 95/100 = 7030
A:B:C = 6500*6 : 8400*5 : 10,000*3 ===> 39:42:30
Share of B= 7030*42/111 =  Rs. 2660
3. E)State A and State B had an equal number of candidates appeared.
In state A, candidates got selected = 6%
In state B, candidates got selected = 7%
Difference between the selected candidates from state A and B = 1%
This 1% is given which is equal to = 80
So, 100% will be equal to = 80*100 = 8000
Total appeared candidates in State A = total appeared candidates in State B = 8000
4. E)Let total voters = V
No. of voters who cast their vote = 0.9*V
Valid votes = 0.9*0.9*V = 0.81*V
Winner got 54%& loser got 46% i.e a difference of 8% or 0.08.
0.08 * (0.81*V) = 1620
V = 25000.
5. C)Let the number of persons eligible to vote be x. Then,
Number of eligible persons between 18 and 21 = 8% of x
Number of persons between 18 and 21, who voted = 85% of (8% of x)
= 85/100 * 8/100 * x = 68x/1000
Required percentage = 68x/1000 * 1/x * 100 = 6.8%
6. E)Let the monthly salary of Pragya be Rs. ‘a’.
Then, [100-(25+20)]% of [100-(24+15)]% of a = 10736
55% of 61% of a = 10736 ————–> a = 32000
7. A)Let CP = Rs 100, P = 30.05%
∴ S.P. = Rs 130.05
Discounts = 10%, 15%, 15%∴ M.P. = 130.05 × 100/90 x 100/85 x 100/85 = Rs 200
If discounts are 10% and 15% only
∴ S.P. = M.P. × {(100-d1)/100} x {(100-d2)/100}
=> 200 x 90/100 x 85/100 = Rs. 153
So, Profit = 53%
8. C)Let the speeds of fast plane and slow planes be x and y m/sec respectively D = s × t
If they move in opposite direction
15 (x + y) = 1200 ⇒ x + y = 80 m/sec … (i)
If they move in same direction, relative speed = x – y m/sec
Time = 60 i.e. 4 times
∴ Speed is (1/4)th x – y = 20 m/sec … (ii)
Solving (i) and (ii),
y = 50 m/sec = 0.05 km/sec
9. D)You are starting from Mumbai at 12:00 noon, so you’ll meet first train which is going to reach Mumbai at 12:30pm or which started from Pune at 8:00am. Also you’ll reach Pune at 4:30pm, so you’ll meet the last train which leaves Pune at 4:00pm.
So in all, you are going to meet all trains which start from Pune at 8:00am, 9:00am, 10:00am, 11:00am, 12:00noon, 1:00pm, 2:00pm, 3:00pm and 4:00pm i.e. 9 in total.
10. A) (D/40) – (D/50) = 1 ⇒ D = 200 kms
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