### Practice Aptitude Questions (Mixed Problems) With Solutions Set-55

Practice Aptitude Questions (Mixed Problems) With Solutions Set-55:
Dear Readers, Important Aptitude Questions for SSC/FCI Exam was given here with solutions, candidates those who are preparing for those exams can use this material.

1).The average age of a class of 35 students is 15 years. If the teacher’s age is also included the average age increases by one year. Furthermore, if the average age of the teacher’s family having a wife and a son is 40 years and the son’s age is 80% less than his mother’s age, then the age of the teacher’s wife is
a)    55.5 years
b)    57.5 years
c)    50 years
d)    47.5 years

2). If the amount is 3 (3 / 8) times the sum after 3 years at compound interest compounded annually, then the rate of interest per annum is
a)    33 ( 1 / 3)%
b)    25%
c)    50%
d)    16 ( 2 / 3)%

3).A shopkeeper sells an article at 15% gain. Had he sold it for Rs.18 more, he would have gained 18%. The cost price ( in Rs. ) of the article is
a)    350
b)    540
c)    318
d)    600

4).A cloth merchant on selling 33 metres of cloth obtains a profit equal to the selling price of 11 metres of cloth. The profit is
a)    11%
b)    40%
c)    22%
d)    50%

5).A single discount equivalent to successive discounts of 20%, 10%, and 5% is
a)    36.1%
b)    35%
c)    35.6%
d)    31.6%

6).A, B and C started a business with their investments in the ratio 1 : 2 : 4. After 6 months a increased his capital by 50% and B invested twice the amount as before, while c withdrew 1th / 4 of his own investment. The ratio of their profits at the end of the year was
a)    5 : 14 : 16
b)    10 : 5 : 9
c)    5 : 12 : 14
d)    6 : 9 : 17

7).Two trains 180 metres and 120 metres in length are running towards each other on parallel tracks, one at the rate 65 km/hr and another at 55 km/hr. In how many seconds will they be clear of each other from the moment they meet?
a)    15
b)    6
c)    9
d)    12

8).Three men can complete a piece of work in 6 days. Two days after they started the work, 3 more men joined them. How many days will they take to complete the remaining work?
a)    4 days
b)    1 day
c)    2 days
d)    3 days

9).a metallic sphere of radius 10.5 cm is melted and then recast into small cones each of radius 3.5 cm and height 3 cm. the number of cones thus formed is
a)    126
b)    140
c)    132
d)    112

10).If the ratio of the diameters of two right circular cones of equal height be 3 : 4, then the ratio of their volumes will be
a)    27 : 64
b)    3 : 4
c)    9 : 16
d)    16 : 9

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

Solution:
1).  Total age of the class
= Average  × Total students
= 15 × 35 = 525
When teacher is included, new average = 15 + 1 = 16
Total age of the class and the teacher = 16 × 36 = 576
∴ Age of the teacher = 576 – 525 = 51 years
Let the teacher’s son’s age by x years
Then son’s age = 20% of x
= (20 / 100 )  × x = x / 5
Total age of the teacher’s family = 3 × 40 = 120 years
= 51 + x + (x / 5) = 120
6x / 5 = 120 – 51 = 69
∴ x = (69 × 5) / 6 = 57.5 years
2).  Amount = P [ 1 + ( R / 100) ]n
3 ( 3 / 8 )P = P [ 1 + ( R / 100) ]3
27 / 8 = [ 1 + ( R / 100) ]3
[ 1 + ( R / 100) ]= ( 3 / 2 )= [ 1 + ( 1 / 2) ]3
∴ R / 100 = 1 / 2
R = 100 / 2 = 50%
3). Let the cost price be Rs. X
When the gain is 15%
Selling price = 115% of x = 115x / 100
When the gain is 18%
Selling price = 118% of x = 118x / 100
According to the problem
118x / 100 = (115x / 100) + 18
118x / 100 - (115x / 100) = 18
3x / 100 =18
x = (18 × 100) / 3 = Rs. 600
4). Let the selling price of 1 metre = Rs. 1
Selling price of 33 metres = Rs. 33
Profit on 33 metres = Selling price of 11 metres = Rs. 11
Let the cost price of  33 metres be Rs. X
Then the selling price _ cost price = profit
33 – x =11
x = 33 – 11 = Rs. 22
Profit percent = ( Profit  / Cost price ) × 100
= (11  / 22 ) × 100 = 50%

5).  Let the marked price be Rs. 100
Price after discounts = (80 / 100) × (90 / 100) × (95 / 100) × 100
= 68.4
Required discount = 100 – 68.4 = 31.6%
Single discount equal to three successive discounts A% , B% , and C% is
100 – {[ (100 – A) (100 – B) (100 – C)] / 100 × 100}
In this problem required discount
= 100 – {[(100 – 20) (100 – 10) (100 – 5)] / 100 × 100}
= (80 × 90 × 95) / 100 × 100
= 100 – 68.4 = 31.6%
6).  Let the investment of A, B, C be x, 2x, and 4x respectively
Profit ratio [ 6x + 6 × (150x / 100)] : ( 6 × 2x + 6 + 4x)
( 6 × 4x + 6  3x)
(6x +9x) : 36x : 42x
15x : 36x : 42x
5 : 12 : 14
7).  Speed of the first train = 65 km/hr. =  65 × m/sec.
Speed of the sdcong train = 55 km/hr. =  55 × (5 /18) m/sec.
Time taken to cross each other
= Sum of the length of the trains / Sum of the Speeds
= (180 + 120) / [(65 + 55) × ( 5 / 18)]
= (300 × 18) / (120 × 5) = 9 Sec.
8). 3 m can complete a work in 6 days
∴ 3 men’s one day’s work = 1 / 6
3 men’s two day’s work = 2 / 6 = 1 / 3
Remaining work = 1 – (1 / 3) = 2 / 3
6 men’s one day’s work = 2 × 3 men’s two day’s work
= 2 × (1 / 6) = 1 / 3
∴ Time take to complete the remaining work by 6 men = ( 2 / 3) / (1 / 3)
= 2 days
SHORT-CUT :
3 men complete the remaining work in 6 – 2 = 4 days                                                               6 men complete the remaining work in ( 3 / 6 ) × 4
=  2 days ( Indirect Proportion )
9).  Volume of the sphere = (4 / 3) πr3
= (4 / 3) π  ( 10.5 )3
Volume of a cone = (1 / 3) πr2 h
= (1 / 3) π × (3.5)2 × 3
Required number of cones = [(4 / 3) π  ( 10.5 )3] / [(1 / 3) π × (3.5)2 × 3]
= (4 × 10.5 × 10.5 × 10.5) / (3.5 × 3.5 × 3) = 126