A man invest some money party in 3% stock at 96 and party in 4% stock at 120. To get equal dividend from both, he must invest the money in the ratio?

Ratio of Speed = 2 : 3 : 4
Ratio of time taken = (1/2) : (1/3) : (1/4) = 6 : 4 : 3

Clearly, If 60 % is equally divided then remaining 40% of total profit will be divided between 2 persons A and B in ratio of (profit of A) : (profit of B)= 12,500 : 8500 = 125 : 85 = 25:17
now difference in amount = 25-17 = 8 this difference = 240
therefore 40% of total profit = 240*(25+17)/(25-17) = 1260
? 100% profit = 1260 / 40 × 100 = 3150

Given 30% of 500

$$\begin{gathered} = 30 100 x 500 \\ = 30 x 5 \\ = 150 \end{gathered}$$

Hence, 30% of Rs. 500 = Rs. 150.

Here, A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10
? A/D = (A/B) x (B/C) x (C/D)
= (2/3) x (5/7) x (3/10)
= 1/7
? A : D = 1 : 7

           2000 x X 100 + 4000 x Y 100 = 320

and      2000 x X 100 + 10000 x Y 100 = 680

x = 4  and  y = 6

x-y = -2

Given, P/Q = 7/5
? (5P - 2Q) / (3P + 2Q) = (5 x 7 - 2 x 5) / (3 x 7 + 2 x 5)
= (35 - 10) / (21 + 10)
= 25/31

Let the number be 'x'

Then, according to the given data,

  5 2 x - 2 5 x 5 2 x x 100

=  21 25 x 100

= 84%

Let the numbers be p & q

q-p/4 = 4q/6

=> q-4q/6 = p/4

=> 2q/6 = p/4 

=> p/q = 4/3

Let 'M' be the maximum marks in the examination.

Therefore, Madhu got 32% of M = 32M/100 = 0.32M
And Kumar got 42% of M = 42M/100 = 0.42M.
In terms of the maximum marks Kumar got 0.42M - 0.32M = 0.1M more than Madhu. ---- (1)

The problem however, states that Kumar got 16 marks more than the cut-off mark and Madhu got 8 marks less than the cut-off mark. Therefore, Kumar has got 16 + 8 = 24 marks more than Madhu. ---- (2)

Now, Equating (1) and (2), we get
0.1M = 24 => M = 24/0.1 = 240
'M' is the maximum mark and is equal to 240 marks.
We know that Madhu got 32% of the maximum marks.
Therefore, Madhu got 32 x 240/100 = 76.8 marks.
We also know that Madhu got 8 marks less than the cut-off marks.

Therefore, the cut-off marks will be 8 marks more than what Madhu got
= 76.8 + 8 = 84.8.

This can be solved as

$$\begin{gathered} 20 1 - 4 20 2 = 20 1 - 1 5 2 \\ = 20 4 5 2 \\ = 20 16 25 \\ = 64 5 \\ = 12 . 8 \end{gathered}$$