Exams

Let the number of failed students be x

=> Number of passed students = 4x 

So total number of students was 5x

From the given data,

If total number of students be 5x – 35

=> 4x-35-9/x+9 = 2/1

=> 4x – 44 = 2(x + 9)

=> 4x – 2x = 18 + 44

=> x = 31

Total number = 31×5

= 155

ROUTINE IS 7 LETTER WORD.. (1st=R,2nd=O,3rd=U,4th=T,5th=I,6th=N,7th=E)
1st and 3rd letter interchanging. (UORTINE)
5th and 7th letter interchanging. (UORTENI)
1st letter shifting one after that (VORTENI)
2nd letter shifting two befor that (VMRTENI)
3rd letter remains same (VMRTENI)
4th letter
(total alphabets - current)+1
(26 - 20)+1= 7.(i.e) G (VMRGFNI)
5th letter shifting one after that (VMRGFNI)
6th letter shifting two befor that (VMRGFLI)
7th letter remains same (VMRGFLI
Like that,
CRUELTY IS 7 LETTER WORD.. (1st=C,2nd=R,3rd=U,4th=E,5th=L,6th=T,7th=Y)
1st and 3rd letter interchanging. (URCELTY)
5th and 7th letter interchanging. (URCEYTL)
1st letter shifting one after that (VRCEYTL)
2nd letter shifting two befor that (VPCEYTL)
3rd letter remains same (VPCEYTL)
4th letter
(total alphabets - current)+1
(26 - 5)+1= 22.(i.e) V (VPCVYTL)
5th letter shifting one after that (VPCVZTL)
6th letter shifting two befor that (VPCVZRL)
7th letter remains same (VPCVZRL).

Given ratio of initial investments = 72:43:65 = 105 : 40 : 36.

 Let the initial investments be 105x, 40x and 36x.

∴A:B:C = 105x×4 + 150100×105x×8 : 40x×12 : 36x×12  

               = 1680x : 480x : 432x = 35 : 10 : 9.

Hence, B's share = 21600×1054 = Rs. 4000.

From the information provided we know that,

Principal + 8% p.a. interest on principal for n years = 180 …….. (1)

Principal + 4% p.a. interest on principal for n years = 120 ……… (2)

Subtracting equation (2) from equation (1), we get

4% p.a. interest on principal for n years = Rs.60.

Now, we can substitute this value in equation (2),

i.e Principal + 60 = 120

= Principal = Rs.60.

We know that SI = , where p is the principal, n the number of years and r the rate percent of  interest.

In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.

Therefore, 60 =(60*n*4)/100

=> n = 100/4 = 25 years.

area of theplot = 110 * 65 = 7150 sq.m
area of the plot excluding the path = (110-5)* (65-5) = 6300 sq.m
area of the path = 7150 - 6300 =850 sq.m
cost of gravelling the path = 850 x (80/100) = 680 Rs

Since S.P. = 5 (M.P. - S.P.) => 5 M.P. = 6 S.P.
M.P. = (6/5) S.P.
Since the percentage discount = Percentage profit,
65S.P - S.P65S.P×100 = S.P -C.PC.P×100
Therefore, 1/6 = (S.P/C.P) – 1 => S.P = (7/6) C.P
M.P = 6/5 S.P = 6/5 x 7/6 C.P = 7/5 C.P
Therefore, Ratio of discount to C.P
= (M.P – S.P)/C.P = [{(7/5)C.P - (7/6)C.P} / C.P.]
= 7/30

Therefore, the ratio is 7 : 30