## Fractions

#### Fractions

1. 1/8th part of a pencil is black, half of the remaining is white. If the remaining part is blue and length of this blue part is 31/2cm, then find the length of the pencil ?
1. 6 cm
2. 7 cm
3. 8 cm
4. 9 cm

1. Let the total length of pencil = L cm
Then, black part = L/8
∴ Remaining part = L - L/8 = 7L/ 8
and White part = (7L/8)/2 = 7L/8
∴ Remaining part = L - (L/8 + 7L/16) = 7L/16
∴ length of blue part = 7L/16

##### Correct Option: C

Let the total length of pencil = L cm
Then, black part = L/8
∴ Remaining part = L - L/8 = 7L/ 8
and White part = (7L/8)/2 = 7L/8
∴ Remaining part = L - (L/8 + 7L/16) = 7L/16
∴ length of blue part = 7L/16

According to the question,
7L/16 = 31/2
⇒ 7L/16 = 7/2
∴ L =8

1. In a polling booth, total number of voters is 1575 out of which 0.4 part are male voters. If a candidate gets 0.4 part of female votes, then find how many votes did the candidate get ?
1. 945
2. 756
3. 378
4. 630

1. Number of male voters = 4/10 of 1575 = 4/10 x 1575 = 630
Number of female voters=1575 - 630 = 945

##### Correct Option: B

Number of male voters = 4/10 of 1575 = 4/10 x 1575 = 630
Number of female voters=1575 - 630 = 945

Now, total votes that candidate got = (6/10) x 630 + (4/10) x 945 = 378 + 378 = 756

1. In a village, (5/8)th of the population are adults,half of the adults are male,(4/5)th of adult females are illiterate. if 400 females are illiterate, then the population of the village is ?
1. 2000
2. 1500
3. 1800
4. 1600

1. Let the population of village = N
and adult females = 1/2 x 5N/8 = 5N/16
∴ illiterate females = 4/5 of adult female population
⇒ 400 = 4/5 x 5N/16

##### Correct Option: D

Let the population of village = N
and adult females = 1/2 x 5N/8 = 5N/16
∴ illiterate females = 4/5 of adult female population
⇒ 400 = 4/5 x 5N/16
⇒ N = (400 x 16)/4
∴ N = 1600

1. (1/4)th of number of boys and (3/8)th of number of girls participated in annual sport days in the school. What fractional part of total number of students participated ?
1. 32%
2. 20%
3. 36%

1. Total number of students participated = (B/4 + 3G/4)
∴ Required percentage= (B/4 + 3G/4) / (B+G) x 100%

##### Correct Option: D

Total number of students participated = (B/4 + 3G/4)
∴ Required percentage= (B/4 + 3G/4) / (B+G) x 100%

1. A scooter before overhauling requires 2/3 h service time every 45 days,while after overhauling it requires 2/3 h service time every 60 days. what fraction of pre-overhauling service time is saved in the latter case ?
1. 4/3
2. 1/3
3. 3/4
4. 1/4

1. Time required for service before overhauling = 2/3h = 40 min in 45 days
and time required for service after overhualing =2/3h= 40 min in 60 days
Now,LCM of 45 and 60 = 180 days
time required for service before overhauling is 180 days = 40 x

##### Correct Option: D

Time required for service before overhauling = 2/3h = 40 min in 45 days
and time required for service after overhualing =2/3h= 40 min in 60 days
Now,LCM of 45 and 60 = 180 days
time required for service before overhauling is 180 days = 40 x 4 = 160 min
and time required for service before overhauling is 180 days =40 x 3 = 120 min
∴ fraction of time saved = 160 - 120/160 =40/160 = 1/4