L can run 1 km in 10 min while M can run it in 12 min. How many metres start can L give M in a km race, so that the race may end in a dead heat?

Given that P's share : Q 's share = 1/3 : 1/5 = 5 : 3
Here, a = 5, b = 3, N = 1664
P's share = a/(a + b) x N
? = 5/(5 + 3) x 1664 = (5/8) x 1664 = ? 1040

Let the number of candidates appeared from each state be x.

In state A, 6% candidates got selected from the total appeared candidates

In state B, 7% candidates got selected from the total appeared candidates

But in State B, 80 more candidates got selected than State A

From these, it is clear that 1% of the total appeared candidates in State B = 80

=> total appeared candidates in State B = 80 x 100 = 8000

=> total appeared candidates in State A = total appeared candidates in State B = 8000

63.5% of 8924.2 +? % of 5324.4 = 6827.5862

=> 63.5% of 8925 + ? % of 5325 = 6830

=> 6830 ~= 5320 + ?(5325)/100

=> ? ~= 22

Given 

4 4 5 of 229 . 79 = ? of 2398 . 51

$$\begin{gathered} 24 5 x 230 = ? x 2400 \\ 24 x 46 = ? x 2400 \\ ? = 46 / 100 \\ ? = 23 50 \end{gathered}$$

The original fraction is   25 51 × 350 + 100 150 + 100  = 15/17.

Since there are 70 males out of 120 applicants, there must be 50 females out must have For the minimum number of males to have a driver's licence all 50 females must have a driver's license Thus the number of males having a driver's licence will be 80 - 50 = 30. The maximum possible number of males having a driver's license is 70. The ratio between the minimum and the maximum is 30 : 70 or 3 : 7 .

Here, x = 20 and y = - 20
Therefore, the net % change in value
= x + y + x y 100 %
=  20 + - 20 + 20 × - 20 100%  or  - 4%

Since the sign is negative, there is a decrease in value by 4%.

Given the company has 8 SD + 6 SRP + 7 IN = 21 cars + 'x' small cars.
Given SD makes 1/4 th of the total fleet.
=> 8 = 1/4 (21 + x)
=> 32 = 21 + x
=> x = 11
Therefore, the company has 11 small cars.

Given that, x/2y = 6/7
? x/y = 12/7
By componenod dividendo,
(x - y) / (x + y) = (12 - 7) / (12 + 7) = 5/19
? (x - y) / (x + y) + 14 /19 = 5/19 + 14/19 = 19/19 = 1