Quantitative Aptitude - Arithmetic Ability Questions

Let the present age of Raj and Rajitha be 4x and 9x.
Then, according to question,
9x = 2(9x-12)-3 => 9x = 27 => x = 3
Raj's present age = 4x = 12yrs,
After 5 years Raj's age will be 12 + 5 = 17 yrs.

Let the two-digit number be 10a + b
a + b = 12 --- (1)
If a>b, a - b = 6
If b>a, b - a = 6
If a - b = 6, adding it to equation (1), we get
2a = 18 => a =9
so b = 12 - a = 3
Number would be 93.
if b - a = 6, adding it to the equation (1), we get
2b = 18 => b = 9
a = 12 - b = 3.
Number would be 39.
There fore, Number would be 39 or 93.

Let the numbers be a and b . Then, a+b =55 and ab = 5 x 120 = 600.

Therefore, Required sum = 1a+1b=a+bab=55600=11120

Let original length = x and original breadth = y.

Original area = xy.

New length = x/2 and New breadth = 3y.

New area = (x/2 * 3y) = (3/2 )xy

Therefore,  Increase % = [(1/2)xy * (1/xy) * 100] % = 50%

Number of words with 5 letters from given 9 alphabets formed = 95

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is = 9P5

Number of words can be formed which have at least one letter repeated =  95 - 9P5

= 59049 - 15120

= 43929

Money lent to A+B = (300 + 540) = Rs. 840 

Amount received = Rs. 1032 

Interest received = Rs. 1032 - Rs.840 = Rs. 192

Interest on Rs. 300 lent to A for 1 year = 300×1×4100 = Rs. 12 

Interest on Rs.540 lent to B for 1 year = 540×6×1100 = Rs. 36 

Total yearly interest = Rs.(12+36) = Rs.48 

If interest is Rs. 48, time = 1 year 

If interest is Rs. 192, time =  192/48 = 4 years 

Let the actual distance be t kms

Now, According to the data,

$$\begin{gathered} 5t + 860 = 6t \\ => 560t + 860 = 6t \\ => 60t + 8 = 72t \\ => 8 = 12t \\ => t = 8/12 = 2/3 hrs \end{gathered}$$

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.