## 24 Sep 2016

### Mission IBPS PO 2016 - Practice Quantitative Aptitude Questions with Detailed Solutions

Mission IBPS PO 2016 - Practice Quantitative Aptitude Questions:
Dear Readers, Important Practice Aptitude Questions for IBPS PO and Upcoming Exams was given here with Solutions. Aspirants those who are preparing for the examination can use this.
1). A man can row 15 km/hr in still water. It takes him twice as long to row upstream as to row downstream. Find the rate of stream?
a)    5 km/hr
b)    10 km/hr
c)    7.5 km/hr
d)    6 km/hr
e)    8 km/hr

2). The monthly incomes of two persons are in the ratio 5 : 4 and their monthly expenditures are in the ratio 9 : 7. If each person saves Rs. 500 per month, then what are their monthly incomes?
a)    Rs 8000 and Rs 10000
b)    Rs 3750 and Rs 3000
c)    Rs 5000 and Rs 4000
d)    Rs 4500 and Rs 4000
e)    None of the above

3). Two equal sums are lent at the same time at 6% and 5 % simple interest respectively. The former is recovered 24 months earlier than the latter. And the amount in each case is Rs. 2400. Find the sum of money lent initially.
a)    1500
b)    2000
c)    2400
d)    3000
e)    3600

4). The average monthly expenditure of a family was Rs. 2200 during the first 3 months; Rs. 2250 during the next 4 months and Rs. 3120 during the last 5 months of a year. If the total savings during the year were Rs. 1260, then the average monthly income was:
a)    Rs. 2605
b)    Rs. 2680
c)    Rs. 2705
d)    Rs. 2745
e)    Rs. 2595

5). What is the size of the longest pencil that can fit in a box with dimensions 12 cm× 10 cm× 8cm?
a)    15
b)    15.5
c)    17
d)    17.5
e)    18

6). A committee of 5 members is to be formed from 8 men and 5 women. How many committees can be formed if at least 2 women and 1 man have to present in the committee?
a)    800
b)    840
c)    880
d)    920
e)    996

7). A man buys milk at Rs. 2.40 per litre. He adds one-third water to it and sells the mixture at Rs. 2.88 per litre. Find his profit percentage. (Assume water is free).
a)    21%
b)    30%
c)    40%
d)    50%
e)    60%

8). A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the wall?
a)    13/3 days
b)    22/3 days
c)    7/4 days
d)    7 days
e)    None of these

9). The sum of 2 numbers is 216, and their HCF is 27. How many such pairs of numbers exist? (A pair a unique set of 2 numbers, so (a, b) and (b, a) will be considered as 1 pair).
a)    0
b)    1
c)    2
d)    3
e)    4

10). Ajay reads at an average rate of 30 pages per hour, while Vikram reads at an average rate of 40 pages per hour. If Ajay starts reading a novel at 4:30 PM and Vikram begins reading an identical copy of the same book at 5:20 PM, at what time will they be reading the same page?
a)    7:50 PM
b)    8:15 PM
c)    8:40 PM
d)    9:00 PM
e)    9:25 PM

1)a   2)c   3)a   4)c   5)d   6)c   7)e   8)b   9)c   10)a

Solution:
1). Let the man’s upstream speed be x km/hour and downstream speed will be 2x km/hour
Speed in still water = 1/2 (2x + x) = 3x/2 km/hour
3x/2 = 15
X = 10
Hence, his downstream speed = 20km/hour
Rate of stream = 1/2 (20-10) = 5km/hour

2). Let the incomes of two persons be 5x and 4x
let the expenditures of them be 9y and 7y
Each person saves Rs. 500
Therefore,
5x – 9y = 500
4x – 7y = 500
Solving the above equations,
20x – 36y = 2000
20x – 35y = 2500
Y = 500
Therefore,
5x = 500 + 9y
5x = 500 + 9(500) = 5000
X = 1000
Hence, their salaries are Rs. 5000 and Rs. 4000

3). Let the sum be S, time be ‘n’ years for 6%. n+2 years for 5%
2400 = S + S ×n × 6/100
2400 = S + S × (n+2) × 5/100
So, 6n = 5(n+2) or n = 10 years.
2400 = S + S × 10 × 6/100 = 1.6S
S = 2400/1.6 = 1500

4). Total expenditure for first 3 months = 2200 × 3 = Rs 6600
Total expenditure for next 4 months = 2250 × 4 = Rs9000
Total expenditure for last 5 months = 3120 × 5 = Rs 15600
Total expenditure = 6600 + 9000 + 15600 =Rs 31200
Total income = expenditure + savings = 31200 + 1260 = Rs 324060
Average monthly income = 32460/12 = Rs 2705

5). The longest pencil that can be fit will be the diagonal length
Required length = (122 + 102 +82)1/2 ≈17.5cm

6). The various possible cases are:
i. 2 women and 3 men = 5C2 × 8C3 = 10 × 56 = 560
ii. 3 women and 2 men = 5C3 × 8C2 = 10 × 28 = 280
iii. 4 women and 1 men = 5C4 × 8C1 = 5 × 8 = 40
Total = 560 + 280 + 40 = 880

7). Let say he purchases 3 litres of milk whose cost is Rs. 7.20
He adds 1 litre of water and the mixture of 4 litres is sold at Rs 2.88 × 4 = Rs11.52
Profit percentage = (11.52 – 7.20) × 100.0/7.20 = 4.32 × 100.0/7.2 = 60%

8). Amount of work done by A in one day = 1/8th of the total work
B can break 1/3rd of the work in one day
Therefore, if both of them are working together then the work done in one day = 1/8 – 1/3 = -5/24
Negative sign indicates that, work is more broken than built in one day
Amount of work done by A in four days = 1/2 of the  total work
Work done by both A and B for two days = -10/24 = -5/12
Total work done by the end of 6 days = 1/2 - 5/12 = 1/12
Remaining work = 1 – 1/12 = 11/12
Time taken by A to finish 11/12th of the work = 11/12 × 8 = 22/3 days

9). Let the numbers be a,b
A = 27m, b = 27n where m, n are co-prime
27(m + n) = 216, or m+n = 8
M = 1, n = 7 and m = 3, n = 5 are the only 2 co – prime pairs possible.
So we have 2 pairs: (27 , 189) and ( 81, 135)

10). Ajay reads at average rate of 30 pages per hour ie. 1 page in every two minutes.
Therefore, by 5:20 PM, he would have covered 25 pages
By 6:20 PM, Ajay would have read 25+30 pages and Vikram would have read 40 pages.
By 7:20 PM, Ajay would have read 85 pages and Vikram would have read 80 pages
In next half an hour, Ajay would cover 15 pages and he will finish 100 pages
Vikram would cover 20 pages and he will also finish 100 pages
Hence, both of them will be on same page at 7:50