Quantitative Aptitude - Arithmetic Ability Questions

Let the numbers 13a and 13b.

Then, 13a x 13b = 2028

=>ab = 12.

Now, the co-primes with product 12 are (1, 12) and (3, 4).

[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]

So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).

Clearly, there are 2 such pairs.

Suppose B joined for x months . Then,  ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.

So, B joined for 8 months.

Speed =   6005×60 m/sec= 2 m/sec = 2 x (18/5) km/hr = 7.2 km/hr

Let original length = x metres and original breadth = y metres.

Original area = xy sq.m 

Increased length  = 120100 and Increased breadth = 120100 

New area = 120100x*120100y=3625xy m2 

The difference between the Original area  and New area  is:  

3625xy-xy

1125xy Increase % =1125xyxy*100= 44%

Here the given number series is 0, 3, 8, 15, 24, ?

The next number in the given series can be found such a way that the number series follows a pattern,

$$\begin{gathered} 22 - 4 = 0 \\ 32 - 6 = 3 \\ 42 - 8 = 8 \\ 52 - 10 = 15 \\ 62 - 12 = 24 \\ 72 - 14 = 35 \\ Hence, the next number in the iven series is 35. \end{gathered}$$

Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.

Therefore,  Man's rate against the current = (12.5 - 2.5) = 10 km/hr.