Aptitude Test

Polygon: A polygon is a 2-dimensional shape that is formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons.

Let the side is n. because there are n sides, we have to subtract n from total number of line formed by joining two adjacent vertices of polygon.

number of diagonals = ⁿC₂ -n = n(n-1)/2 - n
number of diagonals = n(n-3) / 2 = 44
n² - 3n - 88 = 0
(n+3) (n-11) = 0

n=11 (n can not be negative)
So the number of sides in a shape with 44 diagonals is 11.

Mean=(Total Sum of all the Values)/(No of Values)

The Sum of first ’n' natural numbers is given by,Sum=n*(n+1)/2
then, Mean=[n*(n+1)/2] / n
=n*(n+1) / 2*n

So,the mean of first 100 natural numbers, Mean=100*101 / 2*100
=101/2
=50.5

Suppose x years later the father will be twice as old as his son.
Then, x + 41 = 2 (x + 16)
⇒ x = 41 - 32 = 9 years

Hence the father be twice as old as his son in 9 years

A's 1 day's work = 1/12
B's 1 day's work = 1/12 + 60% of 1/12 = 1/12 x 160/100 = 2/15

Hence,B can do the work in 15/2 days

Let l and b the length and breadth of the rectangle respectively.
Now, according to the question 2(l + b) = 10
l + b = 5 …eq(i)
and lb = 4 …eq(ii)
From Eqs. (i) and (ii), we have
l(5 - l) = 4
5l - l² = 4
l² - 5l + 4 = 0
(l - 4)(l - 1) = 0

length, l = 4 or 1

Let x and y be the length and breadth respectively.
Area of rectangle = x*y
Area of square = (x-4) * (y+3)

As is given , (x-4) * (y+3)= x*y
3x – 4y = 12 ……………………………….(i)

for a square, length = width
(x-4) = (y+3)
x - y = 7 ……………………………….(ii)

Solving eq (i) & (ii) x= 16 and y = 9
Therefore perimeter of rectangle = 2(x+y)= 2(16+9)= 50 cm

Speed(S) = Distance(d)/Time(t)
Rohit's speed = 10 Km/hr = (10 * 5/18) m/sec = 50/18 m/sec

Time taken to cover 800 m = 800 / (50/18) sec = 800 *18 / 50 sec = 288 sec = 4 min 48 sec

Let the numbers are A, B ,C and D, then as given
A+B+C=18*3=54
B+C+D=16*3=48
After resolving the above equations -
A-D=6
the last number is 19 ie D=19
So, A=6+19 =25

Volume = (4/3)πr³
Surface Area = 4πr²

as per question, 4/3 πr³ = 4πr²
⇒ r = 3 units.

5^{1 + x} + 5^{1 - x} = 26
(5*5^x) + (5*5^{- x}) = 26
(5*5^x) + (5/5^x) = 26
5(5^x + 1/5^x) = 26

Let 5^x = y , then
5y² - 26y +5 = 0
5y² - 25y - y + 5 = 0
5y( y - 5) - 1( y - 5) = 0
( y - 5)(5y - 1) = 0
y = 5 , 1/5
that is , 5^x = 5 or 5^-1
therefore x = 1 , -1

(A+B+C)'s one days work= 1/10 + 1/12 + 1/15 = 6+5+4/60 = 15/60 = 1/4
Hence, (A+B+C) can work together in 4 days

6C + 2M = 6 days
36C + 12M = 1 day
As is given 1M = 2C
Then, 36C +12*2C = 1 day
60 children can work in 1 day
Now, 5 men = 10 children
Then, 10 children can work in 6 days.So 5 men also can complete the work in 6 days.

Total Surface Area of a cylinder= 2πrh + 2πr² = 2πr(h + r)
= 2* 22/7 * 4 *(10 + 4)
= 2* 22/7 * 4 * 14
= 2* 22 * 4 * 2
= 352 cm²

A : B = 5 : 2 = 5/2 :1
B : C = 7 : 13 = 1 : 13/7
A : B : C = 5/2 :1 : 13/7 = 35 : 14 : 26
A's part =750 * (35/75) => 350

Let the number be a and b. Then Average is, (a +b) / 2 = 14.5
a + b = 29

as given square root of their product is √ab = 10
ab = 100

(a - b)² = (a + b)² - 4ab
(29)² -(4 *100)= 441
(a - b) = 21
On solving a + b = 29 and a - b = 21, we get a =25 and b = 4.

Cost Price of 100 book will , 10*100 =1000
Selling Price of 100 book will , 12*100 = 1200

So, Profit = SP - CP (if SP > CP),
Profit = 1200 - 1000 = 200 rupees

√2ⁿ = 64
⇒ 2^n/2 = 2⁶
⇒ n/2 = 6
⇒ n = 12

Remember : In such a case , there is always a loss .
Loss%=[common loss or gain%/10]²
=(16/10)²=2.56%

Let x be units digit and y be tens digit.then number is 10y + x
As given,
x + y = 11 ----eq1
10x + y = 10y + x + 27----eq2

from eq2
9x -9y = 27
x - y = 3 ----eq3

by adding eq1 and eq3
2x = 14
x = 7
Substitute x in eq1
7 + y =11
y = 4

Therefore, the number is 10x + y = 10*4 + 7 = 47

If The speed of boat or boatman in calm water is u kmph and The speed of water or stream is v kmph, then:
Speed downstream= (u + v) kmph , In water, the speed along with stream
Speed upstream = (u - v) kmph ,In water, the speed against the stream

15= u + 1.5
⇒ u = 13.5

Speed upstream, u - v = (13.5 - 1.5) km/hr = 12 km/hr