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পরীক্ষা - ১৫

বিষয়: গণিত - ৫
টপিক:
Time & Work; Chain Rule

প্রশ্ন দেখুন অনুশীলন

পেট্রোবাংলা প্রিলি ও লিখিত সমন্বিত প্রস্তুতি [Archived]

পেট্রোবাংলা প্রিলি ও লিখিত সমন্বিত প্রস্তুতি [Archived] · তারিখ অনির্ধারিত · ২৫ প্রশ্ন

১.

12 examiners (men) work 16 hours a day to check 24000 answer sheets in 18 days. Now, 24 examiners would work how many hours per day to check 36000 answer sheets in 36 days?

ক
6 hours
খ
8 hours
গ
12 hours
ঘ
16 hours
ঙ
None of these

ব্যাখ্যা

Question: 12 examiners (men) work 16 hours a day to check 24000 answer sheets in 18 days. Now, 24 examiners would work how many hours per day to check 36000 answer sheets in 36 days?

Solution:
১২ জন ১৮ দিনে ২৪০০০টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে ১৬ ঘণ্টা
১২ জন ১৮ দিনে ১টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে ১৬/২৪০০০ ঘণ্টা
১২ জন ১ দিনে ১টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮)/২৪০০০ ঘণ্টা
১ জন ১ দিনে ১টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮ × ১২)/২৪০০০ ঘণ্টা
২৪ জন ১ দিনে ১টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮ × ১২)/(২৪০০০ × ২৪) ঘণ্টা
২৪ জন ১ দিনে ৩৬০০০টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮ × ১২ × ৩৬০০০)/(২৪০০০ × ২৪) ঘণ্টা
২৪ জন ৩৬ দিনে ৩৬০০০টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮ × ১২ × ৩৬০০০)/(২৪০০০ × ২৪ × ৩৬) ঘণ্টা
= ৬ ঘণ্টা

২.

In the beginning, Rakib works at a rate such that he can finish a piece of work in 24 hrs, but he only works at this rate for 16 hrs. After that, he works at a rate such that he can do the whole work in 18 hrs. If Rakib is to finish this work at a stretch, how many hours will he take to finish this work?

ক
12 hrs
খ
18 hrs
গ
11.5 hrs
ঘ
15 hrs
ঙ
22 hrs

ব্যাখ্যা

Question: In the beginning, Rakib works at a rate such that he can finish a piece of work in 24 hrs, but he only works at this rate for 16 hrs. After that, he works at a rate such that he can do the whole work in 18 hrs. If Rakib is to finish this work at a stretch, how many hours will he take to finish this work?

Solution:
Rakib’s 16 hr work = 16/24 = 2/3.
Remaining work = 1 - 2/3
= 1/3.
Using work and time formula:
This will be completed in (1/3) ×18 = 6 hrs.
So, total time taken to complete work = 16 + 6= 22 hrs.

৩.

A certain number of men can complete a piece of work in 180 days. If there are 30 men less, it will take 20 days more for the work to be completed. How many men were there originally?

ক
135
খ
165
গ
150
ঘ
180
ঙ
300

ব্যাখ্যা

Question: A certain number of men can complete a piece of work in 180 days. If there are 30 men less, it will take 20 days more for the work to be completed. How many men were there originally?

Solution:
Let there be x men originally.
They were to complete the work in 180 days but as the number of persons is reduced to x - 30.
∴ Work takes 20 more days.

So the equation is
180x = (x - 30)200
⇒ 180x = 200x - 6000
⇒ 20x = 6000
⇒ x = 300

৪.

A garrison is provided with ration for 90 soldiers to last for 70 days. For how much more time would the whole ration last if 10 additional soldiers join them after 20 days?

ক
40 days
খ
36 days
গ
30 days
ঘ
56 days
ঙ
45 days

ব্যাখ্যা

Question: A garrison is provided with ration for 90 soldiers to last for 70 days. For how much more time would the whole ration last if 10 additional soldiers join them after 20 days?

Solution:
Let the whole ration now lasts for x days.
Equating the consumption on both sides, we get
(90 × 70) = (90 × 20) + (100 × x)
⇒ 630 = 180 + 100x
⇒ 100x = 450
⇒ x = 45 days.

৫.

A man can walk a certain distance at a uniform speed in 100 days. How long will it take him to cover twice the distance at half the normal speed?

ক
50 days
খ
400 days
গ
200 days
ঘ
12.5 days
ঙ
25 days

ব্যাখ্যা

Question: A man can walk a certain distance at a uniform speed in 100 days. How long will it take him to cover twice the distance at half the normal speed?

Solution:
Earlier time = 100 days.
Distance is doubled and speed is reduced to half.
∴ time will become 2 × 2 = 4 times.
Hence now it will take 100 × 4 = 400 days

৬.

A and B undertake to do a piece of work for Tk. 450. A can do it in 20 days and B can do it in 40 days. With the help of C, they finish it in 8 days. How much should C be paid for his contribution?

ক
Tk. 180
খ
Tk. 40
গ
Tk. 120
ঘ
Tk. 60
ঙ
Tk. 50

ব্যাখ্যা

Question: A and B undertake to do a piece of work for Tk. 450. A can do it in 20 days and B can do it in 40 days. With the help of C, they finish it in 8 days. How much should C be paid for his contribution?

Solution:
A & B would have done 8/20 & 8/40 of the work respectively in 8 days.
Together they have done 3/5th of the work.
This implies that C has done 2/5th of the work.
Thus, C should be paid 2/5th of the amount i.e. 450 × (2/5) = Tk. 180.

৭.

A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?

ক
75 m
খ
25 m
গ
50 m
ঘ
100 m
ঙ
125 m

ব্যাখ্যা

Question: A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?

Solution:
Earlier dimensions of the wall = 100 × 3 × 0.30.
Volume of the wall = 90
New dimensions = L × 1.5 × 0.3.
Volume of the wall = 0.45L
∴ As men, women and children are given to be equally efficient, so in the first case, the total number of persons is (30 + 20 + 50) = 100 and the same in the second case is (15 + 25 + 35) = 75

working 9 hours a day in 20 days 100 persons make 90 m³ wall
∴ working 1 hours a day in 1 days 1 persons make 90/(100 × 20 × 9) m³ wall
∴ working 2 hours a day in 15 days 75 persons make (90 × 75 × 15 × 2)/(100 × 20 × 9) m3 wall
= 11.25

∴ Length of the wall = L = 11.25/0.45 = 25 m

৮.

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

ক
1
খ
3
গ
7
ঘ
14
ঙ
None of these

ব্যাখ্যা

Question: If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

Solution:
7 spiders make 7 webs in 7 days
1 spiders make 1 webs in (7 ×7)/7 days
= 7 days

৯.

Akbar and Vijay undertake to do a piece of work for Tk. 480. Akbar alone can do it in 75 days while Vijay alone can do it in 40 days. With the help of Polash, they finish the work in 25 days. How much should Polash get for his work?

ক
Tk. 40
খ
Tk. 20
গ
Tk. 360
ঘ
Tk. 100
ঙ
Tk. 60

ব্যাখ্যা

Question: Akbar and Vijay undertake to do a piece of work for Tk. 480. Akbar alone can do it in 75 days while Vijay alone can do it in 40 days. With the help of Polash, they finish the work in 25 days. How much should Polash get for his work?

Solution:
In 25 days, Akbar and Vijay would have done 1/3 and 5/8 of the work.
The remaining work is 1 - (1/3 + 5/8) = 1/24.
This means Pradeep has done 1/24th of the work, so he should be paid 1/24th of the amount i.e. 480 × (1/24) = Tk. 20

১০.

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

ক
10
খ
13
গ
14
ঘ
15
ঙ
16

ব্যাখ্যা

Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

Solution:
Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)

∴ 30 × 6 × x = 39 × 5 × 12
⇒ x = (39 × 5 × 12)/(30 × 6)
∴ x = 13

১১.

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in-

ক
4 days
খ
6 days
গ
8 days
ঘ
12 days
ঙ
None of these

ব্যাখ্যা

Question: A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in-

Solution:
Suppose A, B and C take x, x/2 and x/3 days respectively to finish the work.
Then,
1/x + 2/x + 3/x = 1/2
⇒ 6/x = 1/2
⇒ x/6 = 2
∴ x = 12

So, B takes (12/2) = 6 days to finish the work.

১২.

A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

ক
75
খ
82
গ
100
ঘ
110
ঙ
120

ব্যাখ্যা

Question: A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

Solution:
Originally let there be x men.
Less men, More days (Indirect Proportion)
Therefore, (x - 10) : x : : 100 :110
⇒ (x - 10)/x = 100/110
⇒ (x - 10) × 110 = x × 100
⇒ 11x - 110 = 10x
∴ x = 110

১৩.

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

ক
7 hours 30 minutes
খ
8 hours
গ
8 hours 15 minutes
ঘ
8 hours 25 minutes
ঙ
None of these

ব্যাখ্যা

Question: Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

Solution:
Number of pages typed by Ravi in 1 hour = 32/6 = 16/3
Number of pages typed by Kumar in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3

Therefore Time taken by both to type 110 pages = 110 × (3/40) hours
= 33/4 hours
= 8.25 hours
= 8 hour 15 minutes

১৪.

A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

ক
3
খ
5
গ
6
ঘ
9
ঙ
10

ব্যাখ্যা

Question: A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

Solution:
[(100 × 35) + (200 × 5)]men can finish the work in 1 day
Therefore,
4500 men can finish the work in 1 day.
100 men can finish it in 4500/100 = 45 days.

∴ This is 5 days behind Schedule

১৫.

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

ক
40
খ
35
গ
45
ঘ
50
ঙ
None of these

ব্যাখ্যা

Question: 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

Solution:
Let,
1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then,
4x + 6y = 1/8 and 3x + 7y = 1/10
Solving the two equations, we get: x = 11/400 , y = 1/400

∴ 1 woman's 1 day's work = 1/400
10 women's 1 day's work = (1/400) × 10 = 1/40
Hence, 10 women will complete the work in 40 days.

১৬.

2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in-

ক
18 days
খ
21 days
গ
24 days
ঘ
25 days
ঙ
30 days

ব্যাখ্যা

Question: 2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in-

Solution:
(2 × 14) men + (7 × 14) boys = (3 × 11) men + (8 × 11) boys
⇒ 28 men + 98 boys = 33 men + 88 boys
⇒ 5 men= 10 boys
∴ 1man= 2 boys

Therefore,
(2 men + 7 boys) = (2 × 2 +7) boys = 11 boys
(8 men + 6 boys) = (8 × 2 + 6) boys = 22 boys.

Let the required number of days be x.
More boys , Less days (Indirect proportion)
More work , More days (Direct proportion)

Therefore,
(22 × 1 × x) = (11 × 3 × 14)
⇒ x = 21

Hence, the required number of days = 21

১৭.

A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?

ক
11 : 30 A.M.
খ
12 noon
গ
12 : 30 P.M
ঘ
1 : 00 P.M
ঙ
None of these

ব্যাখ্যা

Question: A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?

Solution:
(P + Q + R)'s 1 hour's work = (1/8 + 1/10 + 1/12) = 37/120
Work done by P, Q and R in 2 hours = (37/120) × 2 = 37/60

Remaining work = (1 - 37/60) = 23/60
(Q + R)'s 1 hour's work = (1/10 + 1/12) = 11/60

Now,
11/60 of the work is done by Q and R in 1 hour.
23/60 of work will be done by Q and R in (60/11) × (23/60) = 23/11 hours = 2.09 hours ≈ 2 hours

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

১৮.

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

ক
8
খ
9
গ
10
ঘ
11
ঙ
12

ব্যাখ্যা

Question: 3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution:
Let the required no of working hours per day be x.
More pumps , Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)

∴ (4 × 1 × x) = (3 × 2 × 8)
⇒ x = 12

১৯.

Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

ক
3 : 4
খ
4 : 3
গ
5 : 3
ঘ
Data inadequate
ঙ
None of these

ব্যাখ্যা

Question: Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

Solution:
(20 × 16) = 320 women can complete the work in 1 day.
∴ 1 woman's 1 day's work = 1/320

(16 × 15) = 240 men can complete the work in 1 day.
1 man's 1 day's work = 1/240

So, required ratio = 1/240 : 1/320
= 1/3 : 1/4
= 4 : 3

২০.

If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?

ক
46 meters
খ
47 meters
গ
48 meters
ঘ
49 meters
ঙ
50 meters

ব্যাখ্যা

Question: If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?

Solution:
Let the required length be x meters

More men, More length built (Direct proportion)
Less days, Less length built (Direct Proportion)

∴ (20 × 6 × x)=(35 × 3 × 56)
∴ x = 49

Hence, the required length is 49 m.

২১.

A and B can do a job together in 7 days. A is 1.75 times as efficient as B. The same job can be done by A alone in-

ক
9.33 days
খ
11 days
গ
12.25 days
ঘ
16.33 days
ঙ
None of these

ব্যাখ্যা

Question: A and B can do a job together in 7 days. A is 1.75 times as efficient as B. The same job can be done by A alone in-

Solution:
1.75 = 175/100 = 7/4
(A's 1 day's work) : (B's 1 day's work) = 7/4 : 1 = 7 : 4.
Let A's and B's 1 day's work be 7x and 4x respectively.
Then,
7x + 4x = 1/7
⇒ 11x = 1/7
⇒ x = 1/77

A's 1 day's work = (1/77) × 7 = 1/11
∴ A can do the work in 11 days.

২২.

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is-

ক
29.5
খ
37.25
গ
42
ঘ
54
ঙ
None of these

ব্যাখ্যা

Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is-

Solution:
fter 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.

Now, Less men, More days (Indirect Proportion)
125 : 150 : : 35 : x
⇒ 125/150 = 35/x
⇒ 125 x = 150 × 35
⇒ x = (150 × 35)/125
∴ x = 42.

২৩.

A, B, and C can do a piece of work in 8 days. B and C together do it in 24 days. B alone can do it in 40 days. In what time will it be done by C working alone?

ক
25 days
খ
24 days
গ
60 days
ঘ
20 days
ঙ
30 days

ব্যাখ্যা

Question: A, B, and C can do a piece of work in 8 days. B and C together do it in 24 days. B alone can do it in 40 days. In what time will it be done by C working alone?

Solution:
B & C do this work in 24 days.
B alone does this work in 40 days.

C alone can do work in 1 day 1/24 - 1/40 = 2/120 = 1/60 of the work
∴ C will take 60 days to finish the work.

২৪.

If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

ক
48 paise
খ
54 paise
গ
56 paise
ঘ
72 paise
ঙ
None of these

ব্যাখ্যা

Question: If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

Solution:
Let the required weight be x kg.
Less weight, Less cost (Direct Proportion)
250 : 200 : : 60 : x
⇒ 250/200 = 60/x
⇒ 250x = (200 × 60)
⇒ x = (200 × 60)/250
∴ x = 48.

২৫.

A can do a piece of work in 12 days. B can do this work in 16 days. A started the work alone. After how many days should B join him, so that the work is finished in 9 days?

ক
2 days
খ
3 days
গ
4 days
ঘ
5 days
ঙ
1 day

ব্যাখ্যা

Question: A can do a piece of work in 12 days. B can do this work in 16 days. A started the work alone. After how many days should B join him, so that the work is finished in 9 days?

Solution:
A's work in 9 days = 9/12 = 3/4.
Remaining work = 1 - 3/4 = 1/4.

B can do full work in 16 days
1/4 portion of work was done by B in (1/4) × 16 = 4 days.
∴ B would have joined A after 9 - 4 = 5 days.