1. If the cost of 30 meters of cloth is Rs 345 . Find the cost of 16 meters of this cloth.
(a) 184 (b) 162
(c) 875 (d) 321
Answer:(a)
Solution:
Cost of 30 m of cloth = Rs 345
Cost of 1 m of cloth = Rs 11.5
Cost of 16 meter of cloth = 16 x 11.5 = 184
2. If 4 men or 7 women do a work in 60 days then in how many days will 8 men and 7 women finish the same work
(a) 18 (b) 20
(c) 48 (d) 36
Answer:(b)
Solution :
In this problem, we to calculate the work done by a single men or a single women in one day and then we can easily find the answer to the above problem. We assume that the total work done is 1 unit.
Work done by 4 men in one day = 1/60
Work done by a single men = 1/(60 x 4) = 1/240
Work Done by 7 women in 1 day = 1/60
Work Done by 7 women in 1 day = 1/(60 x 7) = 1/(420)
Now, from the condition given in the problem,
Work done by 8 men and 7 women in a single day is 8 x (1/240) + 7 x(1/420) = 1/30 + 1/60 = 3/60=1/20
Time taken to do the work = 1/1/20 = 20 days.
3. A contractor undertook to do a work in 60 days employed 50 workers to carry the job but after 40 days he found that only half had work had been done now how many more worker should he employ to finish the work in time ?
(a) 81 (b) 50
(c) 20 (d) 26
Answer: (b)
Solution:
The hey here is only half the work is done in 40 days by 50 workers.
Now we will find the work done by a 50 workers in 40 days = (1/2)
And lets say x workers can do the remaining half of the work in 20 days.
the equation thus becomes
X x 20 = 50 x 40
X = 100
And since 50 workers are already employed, The contractor has to rope in 100 - 50 = 50 more workers to do the job.
4. If 6 people spend rs 2400 in 4 months then 2 less people will spend Rs 1600 in how many month?
(a) 4 (b) 6
(c) 63 (d) 24
Answer:(a)
Solution:
6 people spent 2400 in 4 month
6 people will spent in 1 month = 2400/4 = 600
1 person spent in 1 month = 600/6 = 100
Now to find how many month it will take to 4 person to spent 1800.
Since spent of 1 person is 100 and 4 person spent is 100 x 4 = 400
And the month it will take to spent 1800 is = 1600/400 = 4 months
5. If 20 men can complete a work in 3 days while 12 ladies can complete the same work in 12 days .in how many days will 20 men and ladies complete the same work ?
(a) 2/17 (b) 2/5
(c) 36/17 (d) 17/3
Answer:(c)
Solution:
First find the work done by 1 men and 1 lady in 1 day
Lets assume work done is 1 unit.
Now,
Work done by 1 men in 1 day = 1/(20 x 3) = 1/60
and work done by 1 lady in 1 day = 1/(12 x 12 ) = 1/144
Work done by 1 men and 1 lady in 1 day = 1/60 + 1/144 = 17/720
And Work done by 20 men and 20 lady in 1 days = (17/720)x 20 = 17/36
And days it will take to complete the work = 1/(17/36) = 36/17
6. If each boy takes two chocolates a day it will suffice to 7 boys for 12 days if each boy takes three chocolates a day then for how many days will suffice to 8 boys ?
(a) 10 (b) 15
(c) 16 (d) 7
Answer: (d)
Solution:
First calculate the total chocolate availabe.
There are 7 boys and they take 2 chocolate each day for 12 days = 7 x 12 x 2 = 168
Now there are 8 boys now and they each take 3 chocolate each day there total chocolate eaten in day = 24
and they will last 168/24 = 7 days
7. If the rate of exchange is 7.50 dollars for Rs 100 how many dollars be equal to Rs 550 ?
(a) 41.75 (b) 42.75
(c) 41.25 (d) 42.25
Answer: (c)
Solution:
Rate of exchange for 1 dollar = 7.5/100
And for 550 we will get = (7.5/100) x 550 = 41.25 dollars
8. If the weight of 13 meters long rod is 23.4 kg what is the weight of 6 meter long rod ?
(a) 7.1 kg (b) 10.8 kg
(c) 12.4 kg (d)18.0 kg
Answer: (b)
Solution:
First Calculate the weight of 1 m rod = 23.4/13 = 1.8 kg/m
And the weight of 6 m rod is = 1.8 x 6 = 10.8 Kg
10. If a scale of map represents 0.8 cm for 8.8 km if two points in a map are 80.5 cm apart what the actual distance between these points ?
(a) 885.5 km (b) 905 km
(c) 700 km (d) 990 km
Answer:(a)
Solution::
First calculate how much 1 cm represents = 8.8/0.8 Km
Therefore 80.5 cm represents = (8.8/0.8) x 80.5 = 885.5 Km
11. If 45 men can complete work in 30 days working 12 hours a day in how many day work 60 men complete the work working 10 hours days ?
(a) 31 (b) 27
(c) 25 (d) 33
Answer: (b)
Solution:
Work done by 1 men per day per hour = 1(/ 30 x 12 x 45)
Lets say it takes X days to complete the work if they work 10 hours a day and there are 60 men
then, work done by a men per hour comes out to be 1/ ( 10 x 60 x X)
Equating both the equations to get
30 x 12 x 45 = 10 x 60 x X
= > X = 27 days
12. A fort provision for 150 men for 45 days after 10 days 25 men left fort how long will the provision last from that day?
(a) 45 (b) 54
(c) 29 /15 (d) 42
Answer: (d)
Solution:
Total provision in the fort = 150 x 45
After 10 days provision left = 150 x 35 = 5250
Now, there are 125 men left and it will last = 5250/125 = 42 days
There fore the provision will last 42 days more after 25 men left.
13. If 6 men weave 168 shawls in 7 days how many shawls will be woven by 8 men is 5 days ?
(a) 126 (b) 90
(c) 160 (d) 104
Answer: (c)
Solution:
Shawls woven in 1 day by the 6 men = 168/7 = 24
And Shawls woven in 1 day by 1 men = 24/6 = 4 shawls
Therefore ,
8 men will weave 4 x 8 = 32 shawls in 1 day
and in 5 days they will weave 5 x 32 = 160 shawls.
14. If 51 people can eat some food in 50 days how many days will the same food be eaten 50 people ?
(a) 52 (b) 51
(c) 50 (d) 55
Answer: (b)
Solution:
Since Total food remains the same which is 51 people X 50 men.
Now there are 50 people there days = 51x 50 / 50 = 51 days
16. If 15 oxen or 20 cows can eat the grass of a field in 80 days then in how many days will 6 oxen and 2 cows eat the same grass ?
(a) 40 (b) 60
(c) 100 (d) 160
Answer:
Solution:
grass eaten by 1 oxen in 1 day = 1/(15 x 80)
grass eaten by 1 cow in 1 day = 1/(20 x 80)
Let it takes x days to eat the grass, then
x { 6/1200 + 2/1600) = x ( 30/4800) = x (1/160) = 1
And therefore x = 160 days
17. A contractor undertook at do a work in 80 days he employed 30 men to carry out the job but after 50 days he found that only half work had been done now how many more men should he employ to finish the work in time ?
(a) 30 (b) 50
(c) 20 (d) 10
Answer: (c)
Solution:
Half work was done in 50 days employing 30 men
And lets says he employs a total of M men to complete the rest of the half work in 30days
Then
M x 30 = 50 X 30
M = 50 men
And men that were added to complete the work in time = 50 30 = 20
18. A family has provision for 15 people for 1 week for if after 2 days 5 people are increased and the ration is reduced by 25 % per person how long will the provision last ?
(a) 5 (b) 6
(c) 7 (d) 4
Answer:
Solution:
Lets ration per day is R then accodring to the conditions given in the above problem, we have
15 x 7 x R = 15 x R x 2 + 20 x 0.75R x D
105 = 30 + 15 D
D = 5
Therefore Ration will last 5 more days after intial 2 days are over. Therefore total days = 7 days
19. A regular working day is 8 hours and regular week is 5 working days .A man is paid rs 2.40 per regular hour and rs 3.20 per hour overtime if he earns rs 432 in 4 week what is the total number of hours he works ?
(a) 180 (b) 195
(c) 160 (d) 175
Answer: (d)
Solution:
Total hours in 4 weeks for a regular week = 8 x 5 x 4 = 160 hours
Amount he should get without overtime = 160 x 2.4 = 384
He got 432, an extra 48 have come due to overtime. Rate of overtime is 3.20
Therefore overtime is done for 48/3.2 = 15 hours
Therefore total hours = 160 + 15 = 175
20. If one fourth kg of a substance costs rs 0.80 what will be the cost of 200 gram of the same substance ?
(a) 40 praise (b) 100 praise
(c) 64 praise (d) 60 praise
Answer: (c)
Solution:
Cost of 1/4 kg of substance = 0.80
Cost of 1 kg of substance = 0.80/.25 = 3.2
And therefore cost of 200 g = 3.2 X .2 = 0.64
21. If 3/5 of a work is done by 12 men in 10 days how many men will complete the whole work in 20 days ?
(a) 9 (b) 8
(c) 10 (d) 7
Answer:
Solution:
Total work done would have been done in (5/3) x 12 x 10 days
Let M men could complete the work in 20 days
Then,
Equating both the terms
We have,
(5/3) x 12 x 10 = M x 20
=> M= 10 men
22. 400 persons working 9 hours a day complete 1/4 the of a piece of work in 10 days the number of additional persons working 8 hours a day required to complete the remaining work in 20 days is ....(a) 675 (b) 275
(c) 250 (d) 225
Answer: (b)
Solution:
work done by 400 person working 9 hours a day for 10 days = 400 x 9 x 10 = 1/4 of total work
Let total work be T
Then T= 4 x 400 x 9 x 10
And work remaining = 3/4 T= (3/4) x 4 x 400 x 9x 10
Again Let M be the number of total men after the addition of men to complete the work in 20 days, then
(3/4) x 4 x 400 x 9 x 10 = M X 20 x 8
108000 = M x 160
M = 675
Therefore Men increased by = 675 - 400 = 275
Solved Problems on spee, time and distance
(a) 184 (b) 162
(c) 875 (d) 321
Answer:(a)
Solution:
Cost of 30 m of cloth = Rs 345
Cost of 1 m of cloth = Rs 11.5
Cost of 16 meter of cloth = 16 x 11.5 = 184
2. If 4 men or 7 women do a work in 60 days then in how many days will 8 men and 7 women finish the same work
(a) 18 (b) 20
(c) 48 (d) 36
Answer:(b)
Solution :
In this problem, we to calculate the work done by a single men or a single women in one day and then we can easily find the answer to the above problem. We assume that the total work done is 1 unit.
Work done by 4 men in one day = 1/60
Work done by a single men = 1/(60 x 4) = 1/240
Work Done by 7 women in 1 day = 1/60
Work Done by 7 women in 1 day = 1/(60 x 7) = 1/(420)
Now, from the condition given in the problem,
Work done by 8 men and 7 women in a single day is 8 x (1/240) + 7 x(1/420) = 1/30 + 1/60 = 3/60=1/20
Time taken to do the work = 1/1/20 = 20 days.
3. A contractor undertook to do a work in 60 days employed 50 workers to carry the job but after 40 days he found that only half had work had been done now how many more worker should he employ to finish the work in time ?
(a) 81 (b) 50
(c) 20 (d) 26
Answer: (b)
Solution:
The hey here is only half the work is done in 40 days by 50 workers.
Now we will find the work done by a 50 workers in 40 days = (1/2)
And lets say x workers can do the remaining half of the work in 20 days.
the equation thus becomes
X x 20 = 50 x 40
X = 100
And since 50 workers are already employed, The contractor has to rope in 100 - 50 = 50 more workers to do the job.
4. If 6 people spend rs 2400 in 4 months then 2 less people will spend Rs 1600 in how many month?
(a) 4 (b) 6
(c) 63 (d) 24
Answer:(a)
Solution:
6 people spent 2400 in 4 month
6 people will spent in 1 month = 2400/4 = 600
1 person spent in 1 month = 600/6 = 100
Now to find how many month it will take to 4 person to spent 1800.
Since spent of 1 person is 100 and 4 person spent is 100 x 4 = 400
And the month it will take to spent 1800 is = 1600/400 = 4 months
5. If 20 men can complete a work in 3 days while 12 ladies can complete the same work in 12 days .in how many days will 20 men and ladies complete the same work ?
(a) 2/17 (b) 2/5
(c) 36/17 (d) 17/3
Answer:(c)
Solution:
First find the work done by 1 men and 1 lady in 1 day
Lets assume work done is 1 unit.
Now,
Work done by 1 men in 1 day = 1/(20 x 3) = 1/60
and work done by 1 lady in 1 day = 1/(12 x 12 ) = 1/144
Work done by 1 men and 1 lady in 1 day = 1/60 + 1/144 = 17/720
And Work done by 20 men and 20 lady in 1 days = (17/720)x 20 = 17/36
And days it will take to complete the work = 1/(17/36) = 36/17
6. If each boy takes two chocolates a day it will suffice to 7 boys for 12 days if each boy takes three chocolates a day then for how many days will suffice to 8 boys ?
(a) 10 (b) 15
(c) 16 (d) 7
Answer: (d)
Solution:
First calculate the total chocolate availabe.
There are 7 boys and they take 2 chocolate each day for 12 days = 7 x 12 x 2 = 168
Now there are 8 boys now and they each take 3 chocolate each day there total chocolate eaten in day = 24
and they will last 168/24 = 7 days
7. If the rate of exchange is 7.50 dollars for Rs 100 how many dollars be equal to Rs 550 ?
(a) 41.75 (b) 42.75
(c) 41.25 (d) 42.25
Answer: (c)
Solution:
Rate of exchange for 1 dollar = 7.5/100
And for 550 we will get = (7.5/100) x 550 = 41.25 dollars
8. If the weight of 13 meters long rod is 23.4 kg what is the weight of 6 meter long rod ?
(a) 7.1 kg (b) 10.8 kg
(c) 12.4 kg (d)18.0 kg
Answer: (b)
Solution:
First Calculate the weight of 1 m rod = 23.4/13 = 1.8 kg/m
And the weight of 6 m rod is = 1.8 x 6 = 10.8 Kg
10. If a scale of map represents 0.8 cm for 8.8 km if two points in a map are 80.5 cm apart what the actual distance between these points ?
(a) 885.5 km (b) 905 km
(c) 700 km (d) 990 km
Answer:(a)
Solution::
First calculate how much 1 cm represents = 8.8/0.8 Km
Therefore 80.5 cm represents = (8.8/0.8) x 80.5 = 885.5 Km
11. If 45 men can complete work in 30 days working 12 hours a day in how many day work 60 men complete the work working 10 hours days ?
(a) 31 (b) 27
(c) 25 (d) 33
Answer: (b)
Solution:
Work done by 1 men per day per hour = 1(/ 30 x 12 x 45)
Lets say it takes X days to complete the work if they work 10 hours a day and there are 60 men
then, work done by a men per hour comes out to be 1/ ( 10 x 60 x X)
Equating both the equations to get
30 x 12 x 45 = 10 x 60 x X
= > X = 27 days
12. A fort provision for 150 men for 45 days after 10 days 25 men left fort how long will the provision last from that day?
(a) 45 (b) 54
(c) 29 /15 (d) 42
Answer: (d)
Solution:
Total provision in the fort = 150 x 45
After 10 days provision left = 150 x 35 = 5250
Now, there are 125 men left and it will last = 5250/125 = 42 days
There fore the provision will last 42 days more after 25 men left.
13. If 6 men weave 168 shawls in 7 days how many shawls will be woven by 8 men is 5 days ?
(a) 126 (b) 90
(c) 160 (d) 104
Answer: (c)
Solution:
Shawls woven in 1 day by the 6 men = 168/7 = 24
And Shawls woven in 1 day by 1 men = 24/6 = 4 shawls
Therefore ,
8 men will weave 4 x 8 = 32 shawls in 1 day
and in 5 days they will weave 5 x 32 = 160 shawls.
14. If 51 people can eat some food in 50 days how many days will the same food be eaten 50 people ?
(a) 52 (b) 51
(c) 50 (d) 55
Answer: (b)
Solution:
Since Total food remains the same which is 51 people X 50 men.
Now there are 50 people there days = 51x 50 / 50 = 51 days
16. If 15 oxen or 20 cows can eat the grass of a field in 80 days then in how many days will 6 oxen and 2 cows eat the same grass ?
(a) 40 (b) 60
(c) 100 (d) 160
Answer:
Solution:
grass eaten by 1 oxen in 1 day = 1/(15 x 80)
grass eaten by 1 cow in 1 day = 1/(20 x 80)
Let it takes x days to eat the grass, then
x { 6/1200 + 2/1600) = x ( 30/4800) = x (1/160) = 1
And therefore x = 160 days
17. A contractor undertook at do a work in 80 days he employed 30 men to carry out the job but after 50 days he found that only half work had been done now how many more men should he employ to finish the work in time ?
(a) 30 (b) 50
(c) 20 (d) 10
Answer: (c)
Solution:
Half work was done in 50 days employing 30 men
And lets says he employs a total of M men to complete the rest of the half work in 30days
Then
M x 30 = 50 X 30
M = 50 men
And men that were added to complete the work in time = 50 30 = 20
18. A family has provision for 15 people for 1 week for if after 2 days 5 people are increased and the ration is reduced by 25 % per person how long will the provision last ?
(a) 5 (b) 6
(c) 7 (d) 4
Answer:
Solution:
Lets ration per day is R then accodring to the conditions given in the above problem, we have
15 x 7 x R = 15 x R x 2 + 20 x 0.75R x D
105 = 30 + 15 D
D = 5
Therefore Ration will last 5 more days after intial 2 days are over. Therefore total days = 7 days
19. A regular working day is 8 hours and regular week is 5 working days .A man is paid rs 2.40 per regular hour and rs 3.20 per hour overtime if he earns rs 432 in 4 week what is the total number of hours he works ?
(a) 180 (b) 195
(c) 160 (d) 175
Answer: (d)
Solution:
Total hours in 4 weeks for a regular week = 8 x 5 x 4 = 160 hours
Amount he should get without overtime = 160 x 2.4 = 384
He got 432, an extra 48 have come due to overtime. Rate of overtime is 3.20
Therefore overtime is done for 48/3.2 = 15 hours
Therefore total hours = 160 + 15 = 175
20. If one fourth kg of a substance costs rs 0.80 what will be the cost of 200 gram of the same substance ?
(a) 40 praise (b) 100 praise
(c) 64 praise (d) 60 praise
Answer: (c)
Solution:
Cost of 1/4 kg of substance = 0.80
Cost of 1 kg of substance = 0.80/.25 = 3.2
And therefore cost of 200 g = 3.2 X .2 = 0.64
21. If 3/5 of a work is done by 12 men in 10 days how many men will complete the whole work in 20 days ?
(a) 9 (b) 8
(c) 10 (d) 7
Answer:
Solution:
Total work done would have been done in (5/3) x 12 x 10 days
Let M men could complete the work in 20 days
Then,
Equating both the terms
We have,
(5/3) x 12 x 10 = M x 20
=> M= 10 men
22. 400 persons working 9 hours a day complete 1/4 the of a piece of work in 10 days the number of additional persons working 8 hours a day required to complete the remaining work in 20 days is ....(a) 675 (b) 275
(c) 250 (d) 225
Answer: (b)
Solution:
work done by 400 person working 9 hours a day for 10 days = 400 x 9 x 10 = 1/4 of total work
Let total work be T
Then T= 4 x 400 x 9 x 10
And work remaining = 3/4 T= (3/4) x 4 x 400 x 9x 10
Again Let M be the number of total men after the addition of men to complete the work in 20 days, then
(3/4) x 4 x 400 x 9 x 10 = M X 20 x 8
108000 = M x 160
M = 675
Therefore Men increased by = 675 - 400 = 275
Solved Problems on spee, time and distance
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