Fractions
 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 3^{1}/_{2}cm, then find the length of the pencil ?

 6 cm
 7 cm
 8 cm
 9 cm

View Hint View Answer Discuss in Forum
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/16Correct 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 = 3^{1}/_{2}
⇒ 7L/16 = 7/2
∴ L =8
 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 ?

 945
 756
 378
 630

View Hint View Answer Discuss in Forum
Number of male voters = 4/10 of 1575 = 4/10 x 1575 = 630
Number of female voters=1575  630 = 945Correct 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
 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 ?

 2000
 1500
 1800
 1600

View Hint View Answer Discuss in Forum
Let the population of village = N
Then, adult's population = 5N/8
and adult females = 1/2 x 5N/8 = 5N/16
∴ illiterate females = 4/5 of adult female population
⇒ 400 = 4/5 x 5N/16Correct Option: D
Let the population of village = N
Then, adult's population = 5N/8
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
 (1/4)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 ?

 32%
 20%
 36%
 data inadequate

View Hint View Answer Discuss in Forum
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%
Clearly, given data is inadequate.
 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 preoverhauling service time is saved in the latter case ?

 4/3
 1/3
 3/4
 1/4

View Hint View Answer Discuss in Forum
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 xCorrect 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