Aptitude Test 1
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Aptitude
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 Total number of questions : 15
 Time allotted : 25 minutes.
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 Question 1 of 15
1. Question
1 points.
The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. Find the present age of the father.
CorrectAnswer: Option B
Solution: Let the son’s present age be x years. Then, father’s present age = (3x + 3) years
==> (3x + 3 + 3) = 2 (x + 3) + 10 ==> 3x + 6 = 2x + 16 ==> x = 10.
hence, father’s present age = (3x + 3) = ((3 x 10) + 3) Years = 33 Years.
IncorrectAnswer: Option B
Solution: Let the son’s present age be x years. Then, father’s present age = (3x + 3) years
==> (3x + 3 + 3) = 2 (x + 3) + 10 ==> 3x + 6 = 2x + 16 ==> x = 10.
hence, father’s present age = (3x + 3) = ((3 x 10) + 3) Years = 33 Years.
 Question 2 of 15
2. Question
1 points.
Raman’s salary was decreased by 50% and subsequently increased by 50%. How much percent (%) does he lose?
CorrectAnswer: Option A
Solution: Let the original salary = Rs. 100
New final salary = Rs. 150 of (50% of Rs.100)
==> Rs.((150/100)*(50/100)*100) = Rs.75
Decrease = 25%
IncorrectAnswer: Option A
Solution: Let the original salary = Rs. 100
New final salary = Rs. 150 of (50% of Rs.100)
==> Rs.((150/100)*(50/100)*100) = Rs.75
Decrease = 25%
 Question 3 of 15
3. Question
1 points.
A bag contains 50 Ps, 25 Ps and 10 Ps coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type.
CorrectAnswer: Option C
Solution: Let the number of 50 Ps, 25 Ps and 10 Ps coins be 5x, 9x and 4x respectively.
(5x/2)+( 9x/ 4)+(4x/10) ==> 206 ==> 50x + 45x + 8x = 4120 ==> 1o3x = 4120 ==> x=40.
Number of 50 Ps. coins = (5 x 40) = 200
Number of 25 Ps. coins = (9 x 40) = 360
Number of 10 Ps. coins = (4 x 40) = 160
IncorrectAnswer: Option C
Solution: Let the number of 50 Ps, 25 Ps and 10 Ps coins be 5x, 9x and 4x respectively.
(5x/2)+( 9x/ 4)+(4x/10) ==> 206 ==> 50x + 45x + 8x = 4120 ==> 1o3x = 4120 ==> x=40.
Number of 50 Ps. coins = (5 x 40) = 200
Number of 25 Ps. coins = (9 x 40) = 360
Number of 10 Ps. coins = (4 x 40) = 160
 Question 4 of 15
4. Question
1 points.
Worker a takes 8 hours to do a job. Worker b takes 10 hours to do the same job. How long should it take both a and b, working together but independently, to do the same job?
CorrectAnswer: Option D
Solution: a’s 1 hour’s work = 1/8
b’s 1 hour’s work = 1/10
(a + b)’s 1 hour’s work = (1/8) +(1/10)=9/40
Both a and b will finish the work in 40/9 days.
IncorrectAnswer: Option D
Solution: a’s 1 hour’s work = 1/8
b’s 1 hour’s work = 1/10
(a + b)’s 1 hour’s work = (1/8) +(1/10)=9/40
Both a and b will finish the work in 40/9 days.
 Question 5 of 15
5. Question
1 points.
A train 100 m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line.
CorrectAnswer: Option C
Solution: Speed of the train = (30 x 5/18) m/ sec ==> (25/3) m/sec.
Distance moved in passing the standing man = 100 m.
Required time taken = 100/(25/3) = (100 *(3/25)) sec = 12 sec
IncorrectAnswer: Option C
Solution: Speed of the train = (30 x 5/18) m/ sec ==> (25/3) m/sec.
Distance moved in passing the standing man = 100 m.
Required time taken = 100/(25/3) = (100 *(3/25)) sec = 12 sec
 Question 6 of 15
6. Question
1 points.
A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the river current in km/hr.
CorrectAnswer: Option A
Solution: Rate downstream ==> (15/3 ¾)km/hr ==> (15*4/15) km/hr ==> 4 km/hr.
Rate upstream ==> (5/2 ½)km/hr ==> (5*2/5)km/hr ==> 2 km/hr.
Speed of current ==> 1/2(42) km/hr ==> 1 km/hr
IncorrectAnswer: Option A
Solution: Rate downstream ==> (15/3 ¾)km/hr ==> (15*4/15) km/hr ==> 4 km/hr.
Rate upstream ==> (5/2 ½)km/hr ==> (5*2/5)km/hr ==> 2 km/hr.
Speed of current ==> 1/2(42) km/hr ==> 1 km/hr
 Question 7 of 15
7. Question
1 points.
If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, Find the area of the rectangle.
CorrectAnswer: Option B
Solution: Let length = x and breadth = y, Then,
2 (x + y) = 46 or x + y = 23 and x^{2} + y^{2 } = (17)^{ 2} = 289.
Now, (x + y)^{ 2} = (23)^{ 2} ==> (x^{2} + y^{2}) + 2xy = 529 ==> 289 + 2xy = 529 ==> xy=120
Area ==> xy = 120 cm^{2}
IncorrectAnswer: Option B
Solution: Let length = x and breadth = y, Then,
2 (x + y) = 46 or x + y = 23 and x^{2} + y^{2 } = (17)^{ 2} = 289.
Now, (x + y)^{ 2} = (23)^{ 2} ==> (x^{2} + y^{2}) + 2xy = 529 ==> 289 + 2xy = 529 ==> xy=120
Area ==> xy = 120 cm^{2}
 Question 8 of 15
8. Question
1 points.
A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.
CorrectAnswer: Option C
Solution: Distance covered in one revolution =((88 x 1000)/1000)= 88m
2∏r = 88 ==> 2 x (22/7) x r = 88 ==> r = 88 x (7/44) = 14 m
IncorrectAnswer: Option C
Solution: Distance covered in one revolution =((88 x 1000)/1000)= 88m
2∏r = 88 ==> 2 x (22/7) x r = 88 ==> r = 88 x (7/44) = 14 m
 Question 9 of 15
9. Question
1 points.
How many words can be formed by using all letters of the word ‘daughter’ so that the vowels always come together?
CorrectAnswer: Option A
Solution: Given word contains 8 different letters. When the vowels aue are always together, we may suppose them to form an entity, treated as one letter.
Then, the letters to be arranged are dgntr (aue).
Then 6 letters to be arranged in ^{6}p_{6} = 6! = 720 ways.
The vowels in the group (aue) may be arranged in 3! = 6 ways.
Required number of words = (720×6) = 4320.
IncorrectAnswer: Option A
Solution: Given word contains 8 different letters. When the vowels aue are always together, we may suppose them to form an entity, treated as one letter.
Then, the letters to be arranged are dgntr (aue).
Then 6 letters to be arranged in ^{6}p_{6} = 6! = 720 ways.
The vowels in the group (aue) may be arranged in 3! = 6 ways.
Required number of words = (720×6) = 4320.
 Question 10 of 15
10. Question
1 points.
In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
CorrectAnswer: Option D
Solution: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (^{6}c_{3}x^{5}c_{2}) = [6x5x4/3x2x1] x [5×4/2×1] = 200.
IncorrectAnswer: Option D
Solution: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (^{6}c_{3}x^{5}c_{2}) = [6x5x4/3x2x1] x [5×4/2×1] = 200.
 Question 11 of 15
11. Question
1 pointsCorrectAnswer: Option C
Solution: The given sequence is +5, +7, +9, —
i.e. ==> 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23,
Missing Number = 23 + 11 = 34IncorrectAnswer: Option C
Solution: The given sequence is +5, +7, +9, —
i.e. ==> 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23,
Missing Number = 23 + 11 = 34  Question 12 of 15
12. Question
1 pointsCorrectAnswer: Option B
Solution:
Numbers are alternatively multiplied by 3 and divided by 2.
So, the next number = 54 ÷ 2 = 27
IncorrectAnswer: Option B
Solution:
Numbers are alternatively multiplied by 3 and divided by 2.
So, the next number = 54 ÷ 2 = 27
 Question 13 of 15
13. Question
1 points.
A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th innings.
CorrectAnswer: Option B
Solution: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
==> 16 (x – 3) + 87 = 17x or x = (87 – 48) = 39.
IncorrectAnswer: Option B
Solution: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
==> 16 (x – 3) + 87 = 17x or x = (87 – 48) = 39.
 Question 14 of 15
14. Question
1 pointsCorrectAnswer: Option D
Solution:
Let the required weight be x kg.
Less weight, Less cost (Direct Proportion)
∴ 250 : 200 :: 60 : x ==> 250x x = (200 x 60)
==> x = (200 x 60)/250
x = 48 paise
IncorrectAnswer: Option D
Solution:
Let the required weight be x kg.
Less weight, Less cost (Direct Proportion)
∴ 250 : 200 :: 60 : x ==> 250x x = (200 x 60)
==> x = (200 x 60)/250
x = 48 paise
 Question 15 of 15
15. Question
1 points.
The ratio between the speeds of two trains is 7: 8. If the second train runs 440 kms in 4 hours, then the speed of the first train is:
CorrectAnswer: Option A
Solution: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = (440/4) = 110
x = (110/8) = 13.75
Hence, speed of first train = (7 x 13.75) km/hr = 96.25 km/hrIncorrectAnswer: Option A
Solution: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = (440/4) = 110
x = (110/8) = 13.75
Hence, speed of first train = (7 x 13.75) km/hr = 96.25 km/hr