Aptitude Questions and Answers
If each edge of a cube is increased by 50%, find the percentage increase in its surface area.
Let the edge = `a` cm
So increase by `50%` = `a+a/2 = 3a/2`
Total surface Area of original cube = `6a^2`
TSA of new cube = `6(3a/2)^2`
`6 xx 9a^2/4 = 13.5a^2`
Increase in area = `13.5a^2 - 6a^2 = 7.5a^2`
`7.5a^2` Increase % = `(7.5a^2)/(6a^2) xx 100 = 125%`
The diagonal of a rectangle is cm and its area is 20 sq. cm. The
perimeter of the rectangle must be:
`sqrt(l^2+b^2) = sqrt(41)` (or) `l^2+b^2 = 41`
Also, `lb = 20`
`(l+b)^2 = l^2 + b^2 + 2lb`
`= 41 + 40 = 81`
`(l + b) = 9`
Perimeter = `2(l + b) = 18 cm`
An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
Error = 2% while measuring the side of a square.
Let the correct value of the side of the square = 100
Then the measured value = 100 + (2% of 100) = 100 +2 = 102 (∵ error 2% in excess)
Correct Value of the area of the square = 100 × 100 = 10000
Calculated Value of the area of the square = 102 × 102 = 10404
Error = 10404 - 10000 = 404
Percentage Error=4.04%
ErrorActual Value×100=40410000×100=4.04%
A towel, when bleached, lost 20% of its length and 10% of its breadth. What is the percentage of decrease in area?
Solution 1:
Let original length = 100 and original breadth = 100
Then original area = 100 × 100 = 10000
Lost 20% of length
=> New length = Original length - (20% of Original Length)
100- (20% of 100) = 100-20 = 80
Lost 10% of breadth
=> New breadth= Original breadth - (10% of original breadth)
= 100 - (10% of 100) = 100-10 = 90
New area = 80 × 90 = 7200
Decrease in area
= Original Area - New Area
= 10000 - 7200 = 2800
Percentage of decrease in area = `(2800/10000) * 100 = 28%`
The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 800 per sq. metre.
Area = 5.5 × 3.75 sq. metre.
Cost for 1 sq. metre. = Rs. 800
Hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = Rs. 16500
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
Let breadth = x cm
Then length = 2x cm
Area = lb = x × 2x = 2x2
New length = (2x - 5)
New breadth = (x + 5)
New Area = lb = (2x - 5)(x + 5)
But given that new area = initial area + 75 sq.cm.
=> (2x - 5)(x + 5) = 2x2 + 75
=> 2x2 + 10x - 5x - 25 = 2x2 + 75
=> 5x - 25 = 75
=> 5x = 75 + 25 = 100
=> x = 1005 = 20 cm
Length = 2x = 2 × 20 = 40cm
If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m, what is its area?
l - b = 23 ....(Equation 1)
perimeter = 2(l + b) = 206
=> l + b = 103 ....(Equation 2)
(Equation 1) + (Equation 2) => 2l = 23 + 103 = 126
=> l = 1262 = 63 metre
Substituting this value of l in (Equation 1), we get
63 - b = 23
=> b = 63 - 23 = 40 metre
Area = lb = 63 × 40 = 2520 m2
What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
l = 15 m 17 cm = 1517 cm
b = 9 m 2 cm = 902 cm
Area = 1517 × 902 cm2
Now we need to find out HCF(Highest Common Factor) of 1517 and 902.
Hence, HCF of 1517 and 902 = 41
Hence, side length of largest square tile we can take = 41 cm
Area of each square tile = 41 × 41 `"cm"^2`
Number of tiles required = `(1517 * 902)/(41 * 41) = 37 * 22 = 814`
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq. metre.
Area of the floor = (5.5 x 3.75) m2 = 20.625 m2.
Cost of paving = Rs. (800 x 20.625) = Rs.16500.
A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?
Clearly, we have : length(l) = 9 ft.
and l+2b = 37 ft.
i.e., 9+2b = 37
2b = 37-9
2b = 28
So, the breadth(b) = 14 ft.
Area = (l x b) = (9 x 14) sq.ft. =126 sq.ft.