## Fractions

#### Fractions

1. A man reads 3/8 of a book on a day and 4/5 of the remainder on the second day. If the number of pages still unread are 40, then how many pages did the book contain?
1. 300
2. 500
3. 320
4. 350

1. 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]

##### Correct Option: C

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

1. If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%, the resultant fraction is 9/35. What is the original fraction ?
1. 3/10
2. 2/15
3. 3/16
4. 2/7
5. None of the above

1. 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

##### Correct Option: E

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

1. A, B, C and D purchase a gift worth ₹ 60. A pays 1/2 of what others are paying, B pays 1/3rd of what other are paying and C pays 1/4th of what others are paying. What is the amount paid by D ?
1. 14
2. 15
3. 16
4. 13

1. 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)

##### Correct Option: D

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

1. The Numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator, then find the fraction.
1. 3/7
2. 4/8
3. 2/7
4. 3/8

1. Let denominator of fraction = x
Then, numerator = x - 4
∴ Fraction = x - 4/x
Now, according to the question,
8[(x - 4) - 2] = (x + 1)

##### Correct Option: A

Let denominator of fraction = x
Then, numerator = x - 4
∴ Fraction = x - 4/x
Now, according to the question,
8[(x - 4) - 2] = (x + 1)
(x -4) - 2= (x + 1)/8
⇒ x - 6 = x + 1/8
⇒ 8x - 48 = x + 1
⇒ 8x - x = 48 + 1
⇒ 7x = 49
⇒ x = 49/7
∴ x = 7
∴ Fraction = (x - 4)/x
Put the value of x.
∴ Fraction = (7 - 4)/7 =3/7

1. 783 ÷ 9 ÷ 0.75 = ?
1. 130
2. 124
3. 118
4. 116
5. None of the above

1. ? = 783/9 x 0.75 = 116

##### Correct Option: D

? = 783/9 x 0.75 = 116