Quantitative Aptitude - Arithmetic Ability Questions

Let the required fraction be x. Then, (1 / x )- x = 9/20
1 - x^(2) / x = 9 / 20  =>  20 - 20 * x^(2) = 9 * x.
20 * x^(2) + 9 *x - 20 = 0.
=> (4 * x + 5) (5 * x - 4) = 0.
=> x = 4 / 5.

m+nm-n=7xx ⇒mn=4x3x  

Again   mn=12x2 

and         mn =60x  

so, 60x=12x2 ⇒x=5    

=>  m= 20  and    n= 15

Hence,    1m:1n=120:115=3:4

Let the present ages of Ajay and Vijay be 'A' and 'V' years respectively.

=> A - 8 = 4/3 (V - 8) and A + 8 = 6/5 (V + 8)

=> 3/4(A - 8) = V - 8 and 5/6(A + 8) = V + 8

V = 3/4 (A - 8) + 8 = 5/6 (A + 8) - 8

=> 3/4 A - 6 + 8 = 5/6 A + 20/3 - 8

=> 10 - 20/3 = 10/12 A - 9/12 A

=> 10/3 = A/12 => A = 40.

Let original length = x and original breadth = y.  

Decrease in area = xy - 80100x×90100y = (7/25)xy

Decrease % =    (7/25)xy * (1/xy) * 100 = 28%

Given that, 

Number of windows = 50

Each window covering covers 15 windows

=> 50 windows requires 50/15 window coverings

= 50/15 = 3.333

Hence, more than 3 window coverings are required. In the options 4 is more than 3. 

Hence, 4 window coverings are required to cover 50 windows of each covering covers 15 windows.

3 x 3 x 3 x 3 x 30 = 2430. Sum of decimal places = 6

Therefore, 3 x 0.3 x 0.03 x 0.003 x 30 = 0.002430 = 0.00243

Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.

Speed in downstream = 3 x 60/18 = 10 km/hr

Rate of current = (10-9)/2 = 1/2 km/hr.