Sum of three fraction is 2 ¹¹/ ₂₄ . If the greatest fraction is divided by the smallest fraction the result is 7/6, which is greater than the middle fraction by 1/3. Find all the three fractions.

Let the fraction be x, y and z respectively in decreasing order.
Then, according to the question,
x/z = 7/6
? x = 7z/6

And y = 7/6 - 1/3 = 7-2/6 = 5/6

Now, x + y + z = 2¹¹/₂₄
? 7z/6 + 5/6 + z = 59/24
? (13z + 5)/ 6 = 59/24
? 13z = 59/4 - 5 =39/4
? z = 3/4
? x =7z/6 = 7/8
Hence, the fraction are 7/8, 5/6, 3/4.

Let A has ? 200 at the starting of game, then B has ? 100 at the starting of game.
After the game, money left with A = 200 - 200/3 = ? 400/3
? Total money with B = 100 + 200/3 = ? 500/3
Let the fraction of money lost by B = N
Then, 500/3 - N x 500/3 = 400/3 + N x 500/3
? 500/3 - 400/3 = 500N/3 + 500N/3
? 100/3 = 1000N/3
? N = (100/3) x (3/1000) = 1/10
so, the fraction of money lost is 1/10.

Let the weight of vesel = x kg
Then, 1/4 of volume of water = (5.25 - x)kg
Full volume of water = (16.5 - x)
? 4(5.25 - x) = (16.5 - x)
? 21 - 4x = 16.5 - x
? 21 - 16.5 = 3x
? x = 4.5/3 = 1.5 kg

Let the total property = N
Then, property of his daughter = P/7
? Remaining property = P - P/7 = 6P/7
Now, this property is divided among his sons, so that each son gets twice the property of his daughter.
Let number of sons be K.
Then, 6N/7 x K = 2N/7
? K = 3

Let the fraction be N.
Then, N / (13/14) - (13/14) x N = 3/65
? 14N/13 - 13N/14 = 3/65
? (196N - 169N)/182 = 3/65
? 27N/182 = 3/65
? N = (3 x 182) / (27 x 65) = 14/45
So, correct answer will be (13/14) x (14/45) = 13/45

Shantanu's pocket allowance = ? 3832.50
Total days in 2011 (general year) = 365 days
Allowance per day = 3832.5/365 = ? 10.5

Let total length of pencil be x cm.
Then, black part = x/8
Remaining part pencil after black part = x - x/8 = 7x/8
then White part = 1/2 (7x/8)
= 7x/16
Now Remaining part of pencil is blue = total length of pencil - (length of black part + length of white part)
length of blue part of pencil = x - (x/8 + 7x/16)
length of blue part of pencil = x - (2x + 7x)/16
length of blue part of pencil = x - 9x/16
length of blue part of pencil = (16 x - 9x)/16
? Length of blue part = 7x/16;

According to question
Length of blue part = 3¹/₂
7x/16 = 3¹/₂
? 7x/16 = 7/2
? x/16 = 1/2
? x = 16/2
? x = 8 cm

Let the number of pages be p.
Number of pages read on first day = 3p/8
Remaining pages = p - 3p/8 = (8p - 3p)/8 = 5p/8
Number of pages read on second day = 4/5 x 5p/8 = p/2
Now , remaining pages = p - [ 3p/8 + p/2]
= p - [(3p + 4p)/8] = [p- 7p/ 8]
= [(8p - 7p)/ 8] = p/8
According to the question
p/8 = 40
? p = 40 x 8
? p = 320

Let the original fraction be p/q.
Numerator is increased by 200%.
? Numerator = p + 200% of p
= p + 200p/100
= p + 2p
= 3p
and denominator of the fraction is increased by 150%.
Denominator = q + 150q/100
= (100q + 150q)/100
= 250q/100
= 5q/2
Then, according to the question,
3p/5q/2 = 9/35
3p x 2/5q = 9/35
6p/5q = 9/35
? p/q = 9 x 5/35 x 6
p/q = 3/14

Let A, B, C and D pay ?x, ?y, ?z and ?a
According to the question,
x = 1/2(y + z + a)
2x = (y + z + a) ..........(i)
y = 1/3(x + z + a)
3y = (x + z + a) ...........(ii)
z = 1/4(x + y + a)
4z = (x + y + a) ..........(iii)
Also, x + y + z + a = 60 ...............(iv)
Now, put the value of x + y + a = 4z from (iii) in (iv)
Then, 4z + z = 60 ? 5z = 60
? z = 12
Similarly, on putting the value of x + z + a = 3y from (ii) in (iv), we get
3y + y = 60 = ? 4y = 60
? y = 15
Again, on putting the value of (y + z + a) = 2x from (i) in (iv), we get
2x + x = 60 ? 3x = 60
&ther4; x = 20
Now, x + y + z + a = 60
On putting the value of x, y and z, we get
12 + 15 + 20 + a = 60
? a = 60 - 47 = ? 13