## Fractions

#### Fractions

1. A has twice as much money as B. They play together and at the end of the first game B wins one-third of A's money from A, what fraction of the sum that B now has, must A win black in the second game, so that they may have exactly equal money ?
1. 1/3
2. 1/5
3. 1/4
4. 1/10

1. 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

##### Correct Option: D

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.

1. Sum of three fractions is 211/24. 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 ?
1. 3/5, 4/7, 2/3
2. 7/8, 5/6, 3/4
3. 7/9, 2/3, 3/5
4. 7/8, 7/9, 7/10

1. 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

##### Correct Option: B

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.

1. Sum of three fraction is 211/24 . 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.
1. 3/5, 4/7, 2/3
2. 7/8, 5/6, 3/4
3. 7/9, 2/3, 3/5
4. 7/8, 7/9, 7/10
5. None of the above

1. Let the greatest, middle and smallest fraction be P, Q and R respectively in decreasing order.

According to the question.
(Greatest fraction) / (Smallest fraction) = 7/6
⇒ P/R = 7/6
⇒ P = 7R/6 ....(i)
and Q = 7/6 - 1/3 = 7 - 2/6 = 5/6 (ii)

Now, P + Q + R = 211/24 (iii )

Substitute the value of P and Q from Eqs. (i), (ii) and put in Eqs (iii),

##### Correct Option: B

Let the greatest, middle and smallest fraction be P, Q and R respectively in decreasing order.

According to the question.
(Greatest fraction) / (Smallest fraction) = 7/6
⇒ P/R = 7/6
⇒ P = 7R/6 ....(i)
and Q = 7/6 - 1/3 = 7 - 2/6 = 5/6 (ii)

Now, P + Q + R = 211/24 (iii )

Substitute the value of P and Q from Eqs. (i), (ii) and put in Eqs (iii), we get
⇒ 7R/6 + 5/6 + R = 59/24
⇒ (7R + 5 + 6R)/6 = 59/24
⇒ (13R + 5) / 6 = 59/24
⇒ 13R = (59/4) - 5 = 39/4
⇒ R = 39 / (4 x 13)
∴ R = 3/4

On putting the value of R in Eq. (i), we get
P = 7R/6 = (7/6) x (3/4) = 7/8

1. In the year 2011, Shantanu gets ₹ 3832.5 as his pocket allowance. Find his pocket allowance per day.
1. ₹ 9.5
2. ₹ 10.5
3. ₹ 12.5
4. ₹ 11.5
5. None of the above

1. Shantanu's pocket allowance = ₹ 3832.50
Total days in 2011 (general year) = 365 days

##### Correct Option: B

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

1. 1/8 part of a pencil is black and 1/2 part of the remaining is white. If the remaining part is blue and length of this blue part is 31/2 cm, then find the length of the pencil.
1. 6 cm
2. 7 cm
3. 8 cm
4. 9 cm
5. None of the above

1. 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)

put the value and solve the equation.

##### Correct Option: C

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