Aptitude Questions and Answers

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%`

`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`

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%

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%`

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

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

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

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`

Area of the floor = (5.5 x 3.75) m² = 20.625 m².

Cost of paving = Rs. (800 x 20.625) = Rs.16500.

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.