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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes
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Math - 05 - Time & Work, Chain Rule
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৪ প্রশ্ন

১.
A can do a piece of work in 8 days and B can do the same piece of work in 12 days. A and B together complete the same piece of work and get Tk. 200 as the combined wages. B’s share of the wages will be -
  1. ক
    ক) Tk. 75
  2. খ
    খ) Tk. 80
  3. গ
    গ) Tk. 85
  4. ঘ
    ঘ) Tk. 90
ব্যাখ্যা

A's share : B's share = Ratio of their 1 day's work
= 1/8 : 1/12
= 3 : 2.
∴ B's share = Tk. 200 × (2/5)
= Tk. 80.

২.
X, Y, and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days Z alone can finish the same work?
  1. ক
    ক) 12
  2. খ
    খ) 16
  3. গ
    গ) 24
  4. ঘ
    ঘ) 36
ব্যাখ্যা

(X + y)'s 1 day's work = (1/16) + (1/16)
= 2/16
= 1/8
Z's 1 day's work = (X + Y + Z)'s 1 day's work - (X + Y)'s 1 day's work
= 1/6 - 1/8
= 1/24.
∴ Z alone can finish the work in 24 days.

৩.
A fort has provisions for 50 days. If after 10 days they are strengthened by 500 men and the remaining food lasts for 35 days, the number of men originally in the fort were -
  1. ক
    ক) 2500
  2. খ
    খ) 3000
  3. গ
    গ) 3500
  4. ঘ
    ঘ) 4000
ব্যাখ্যা

Let, there be x men originally.
So, x men had provisions for 40 days whereas (x + 500) men consumed it in 35 days.
more men, Less days [Indirect proportion]
∴ (x + 500) : x = 40 : 35
⇒ 35(x+ 500) = 40x
⇒ 5x = 35 × 500
⇒ x = (35 × 500)/5
= 3500.

৪.
A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is -
  1. ক
    ক) 4 days
  2. খ
    খ) 6 days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 18 days
ব্যাখ্যা

Ratio of rates of working of A and B = 2:1
So, ratio of times taken = 1 : 2
∴ A's 1 day's work = (1/6);
B's 1 day's work = 1/12
(A + B)'s 1 day's work = (1/6) + (1/12)
= 3/12
= 1/4
So, A and B together can finish the work in 4 days.

৫.
In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
  1. ক
    ক) 1
  2. খ
    খ) 1/40
  3. গ
    গ) 40
  4. ঘ
    ঘ) 80
ব্যাখ্যা

Let,
The required number of days be x.
Less Cows, More days[Indirect proportion]
Less Bags, Less days [Direct proportion]
Cows(1 : 40), bags(40 : 1)}::40 : x
∴ 1 × 40 × x = 40 × 1 × 40
= 40.

৬.
A can do a piece of work in 10 days working, 8 hours per day. If B is two - thirds as efficient as A, then in how many days can B alone do the same piece of work, working 5 hours per day?
  1. ক
    ক) 15
  2. খ
    খ) 18
  3. গ
    গ) 20
  4. ঘ
    ঘ) 24
ব্যাখ্যা

Time taken by A alone to do the work = (10 × 8)
= 80 hrs.
Since B is two -thirds as efficient as A,
So the time taken by B to do the work
= 80 × (3/2)hrs
= 120 hrs.
∴ Required time = (120/5)
= 24 days.

৭.
Lopa can do a work in 3 days while Rasel can do the same work in 2 days. Both of them finish the work together and get Tk. 150. What is the share of Lopa?
  1. ক
    ক) Tk. 30
  2. খ
    খ) Tk. 60
  3. গ
    গ) Tk. 70
  4. ঘ
    ঘ) Tk. 75
ব্যাখ্যা

Lopa's wages : Rasel's wages
= Lopa's 1 day's work : Rasel's 1 day's work
= 1/3 : 1/2
= 2 : 3
∴ Lopa's share = Tk.(2/5) × 150
= Tk 60.

৮.
A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days required to complete the work is -
  1. ক
    ক) 6(3/5)
  2. খ
    খ) 8(1/2)
  3. গ
    গ) 10(1/5)
  4. ঘ
    ঘ) 13(1/2)
ব্যাখ্যা

B's 3 day's work = (1/21) × 3
= 1/7.
Remaining work = 1 - (1/7)
= 6/7.
(A + B)'s 1 day's work
= (1/14) + (1/21)
= 5/42.
Now, 5/42 work is done by A and B in 1 day.
∴ 6/7 work is done by A and B in (42/5) × (6/7)
= 36/5 days.
Hence, total time taken = 3 + (36/5) days
= 10(1/5) days.

৯.
A, B, and C can do a piece of work in 20, 30, and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
  1. ক
    ক) 12 days
  2. খ
    খ) 15 days
  3. গ
    গ) 16 days
  4. ঘ
    ঘ) 18 days
ব্যাখ্যা

A's 2 day's work = (1/20) × 2
= 1/10
(A + B + C)'s 1 day's work = (1/20) + (1/30) + (1/60)
= 6/60
= 1/10
(A + B + C) work in 3 days = (1/10) + (1/10)
= 1/5.
Now, 1/5 work is done in 3 days.
∴ Whole work is done in (3 × 5)
= 15 days.

১০.
A job can be done by 3 skilled workmen in 20 days or by 5 boys in 30 days. How many days will they take if they work together?
  1. ক
    ক) 8 days
  2. খ
    খ) 10 days
  3. গ
    গ) 11 days
  4. ঘ
    ঘ) 12 days
ব্যাখ্যা

3 men's 1 day's work = 1/20;
5 boy's 1 day's work = 1/30.
(3 men + 5 boys)'s 1 day's work = (1/20) + (1/30)
= 5/60
= 1/12.
∴ 3 men and 5 boys will complete the work in 12 days.

১১.
Seven men can complete a work in 12 days. They started the work and after 5 days, two men left. In how many days will the work be completed by the remaining men?
  1. ক
    ক) 5(1/4)
  2. খ
    খ) 6(1/2)
  3. গ
    গ) 7(2/3)
  4. ঘ
    ঘ) 9(4/5)
ব্যাখ্যা

(7 × 12) men can complete the work in 1 day.
∴ 1 man's 1 day's work = 1/84.
7 men's 5 day's work = (1/12) × 5
= 5/12.
Remaining work = 1 - (5/12)
= 7/12
5 men's 1 day's work = (1/84) × 5
= 5/84.
5/84 work is done by them in 1 days.
7/12 work is done by them in (84/5) × (7/12)
= 49/5 days.
= 9(4/5) days.

১২.
If a typist can type 125 pages, 36 lines each, 11 words to each line in 5 days, how many pages of 30 lines each and 12 words to each line can he type in 6 days?
  1. ক
    ক) 165
  2. খ
    খ) 160
  3. গ
    গ) 145
  4. ঘ
    ঘ) 120
ব্যাখ্যা

প্রতি লাইনে 11 words, প্রতি page এ 36 লাইন বিশিষ্ট 125 pages এ
word আছে 11× 36 × 125
5 দিনে 11 × 36 × 125 words হয়
1 দিনে (11 × 36 × 125)/5 words হয়
∴ 6 দিনে (11 × 36 × 125 × 6)/5 words হয়
= (11 × 36 × 125 × 6)/(5 × 12) lines
= (11 × 36 × 125 × 6)/(5 × 12 ×30) pages
= 165 pages.

১৩.
If 12 men and 16 boys can do apiece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is -
  1. ক
    ক) 2:1
  2. খ
    খ) 3:1
  3. গ
    গ) 3:2
  4. ঘ
    ঘ) 5:4
ব্যাখ্যা

Let, 1 man's 1 day's work = x and
1 boy's 1 day's work = y

Then, 12x + 16y = 1/5
and 13x + 24y = 1/4.

Solving these two equations, we get,
x = 1/100 and
y = 1/200
∴ Required ratio = x : y
= 1/100 : 1/200
= 2 : 1.

১৪.
12 men can do a piece of work in 24 days. How many days are needed to complete the work, if 8 men do this work?
  1. ক
    ক) 28
  2. খ
    খ) 36
  3. গ
    গ) 48
  4. ঘ
    ঘ) 52
ব্যাখ্যা

12 men can do a piece of work in 24 days
⇒ M1 = 12 and D2 = 24
8 men can do this work in D2 days
⇒ M2 = 8
M1D1 = M2D2
⇒ 12 × 24 = 8 × D2
⇒ D2 = (12 × 24)/8
= 36 days.

১৫.
56 men complete a piece of work in 24 days. In how many days can 42 men complete the same piece of work?
  1. ক
    ক) 118
  2. খ
    খ) 32
  3. গ
    গ) 48
  4. ঘ
    ঘ) 98
ব্যাখ্যা

Let,
The required number of days be x.
Less Man, More Days [Indirect proportion]
∴ 42 : 56 :: 24 : x
⇒ 42x = 56 × 24
⇒ x = (56 × 24)/42
⇒ x = 32.

১৬.
If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day; in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day?
  1. ক
    ক) 6
  2. খ
    খ) 7
  3. গ
    গ) 8
  4. ঘ
    ঘ) 9
ব্যাখ্যা

Let,
The required number of days be x.
Less pumps, More days[Indirect proportion]
Less weight, Less days [Direct proportion]
More hours/days, Less days [Indirect proportion]
{Pumps(16 : 18) , Weight (2170 : 1736), Hours/Day(9 :7)} :: 10 : x
∴ (16 × 2170 × 9 × x) = (18 × 1736 × 7 × 10)
⇒ x = (18 × 1736 × 7 × 10)/(16 × 2170 × 9)
= 7.

১৭.
21 binders can bind 1400 books in 15 days. How many binders will be required to bind 800 books in 20 days?
  1. ক
    ক) 7
  2. খ
    খ) 9
  3. গ
    গ) 12
  4. ঘ
    ঘ) 14
ব্যাখ্যা

Let,
The required number of binders is x.
Less books, Less binders [Direct proportion]
More days, Less binders [Indirect proportion]
Books {(1400 : 800) , Days (20 : 15)} :: 21 : x
∴ 1400 × 20 × x = 800 × 15 × 21
⇒ x = (800 × 15 × 21)/(1400 × 20)
= 9.

১৮.
A certain number of artisans can complete a shoe fabrication consignment in 16 days. 8 additional artisans had to be deployed for the same consignment and together they completed it in 4 days less than the earlier estimate. The number of artisans initially employed was -
  1. ক
    ক) 18
  2. খ
    খ) 20
  3. গ
    গ) 24
  4. ঘ
    ঘ) 28
ব্যাখ্যা

Let,
The original number of artisans be x.
More artisans, Less days [Indirect proportion]
∴ (x + 8) : x :: 16 : 12
⇒ 12 (x + 8) = 16x
⇒ 12x + 96 = 16x
⇒ 16x - 12x = 96
⇒ 4x = 96
⇒ x = 96/4
⇒ x = 24.

১৯.
A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm. How many times can it go round a cylinder with radius 20 cm?
  1. ক
    ক) 40
  2. খ
    খ) 49
  3. গ
    গ) 100
  4. ঘ
    ঘ) 120
ব্যাখ্যা

Let,
the required number of rounds be x.
More radius, Less rounds [Indirect proportion]
∴ 20 : 14 :: 70 : x
⇒ (20 × x) = (14 × 70)
⇒ x = (14 × 70)/20
= 49.

২০.
A contractor employed 30 men to do a piece of work in 38 days. After 25 days, he employed 5 men more and the work was finished one day earlier. How many days he would have been behind if he had not employed additional men?
  1. ক
    ক) 1
  2. খ
    খ) 1(1/4)
  3. গ
    গ) 1(3/4)
  4. ঘ
    ঘ) 1(1/2)
ব্যাখ্যা

After 25 days, 35 men complete the work in 12 days.
Thus, 35 men can finish the remaining work in 12 days.
∴ 30 men can do it in (12 × 35)/30
= 14 days.
which is 1 day behind.

২১.
A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?
  1. ক
    ক) 10%
  2. খ
    খ) 15%
  3. গ
    গ) 20%
  4. ঘ
    ঘ) 16.67%
ব্যাখ্যা

প্রথম 5 টি copy এর প্রত্যেকটি দেখতে সময় লাগে = 30/5
= 6 মিনিট
পরের 30 টি copy এর প্রত্যেকটি দেখতে সময় পাবে = 150/30
= 5 মিনিট

বর্তমান রেট - 1/6
কাঙ্ক্ষিত রেট - 1/5
বাড়াতে হবে - 1/30

অতএব, {(1/30) / (1/6)} × 100
= 20% faster হতে হবে ।

২২.
Adults can do a job twice as fast as children. If x adults can complete a job in d days, how many children can do the same job in d + 2 days?
  1. ক
    ক) 2dx/(d + 2)
  2. খ
    খ) (d + 2)x/d
  3. গ
    গ) dx/2(d + 2)
  4. ঘ
    ঘ) (2x + d)/(d - x)
ব্যাখ্যা

x adults = 2x children
to complete in d days 2x children is required.
∴ to complete in (d + 2) days (2x × d)/(d + 2) children is required.

২৩.
55 men can finish a work in 42 days. How many additional men must be engaged to complete the work 9 days earlier?
  1. ক
    ক) 15
  2. খ
    খ) 16
  3. গ
    গ) 17
  4. ঘ
    ঘ) 18
ব্যাখ্যা

42 days এ কাজটি complete করতে লাগে 55 men
1 day এ কাজটি complete করতে লাগে 55 × 42 men
33 day এ কাজটি complete করতে লাগে (55 × 42)/33 men
= 70 men.
Additional men লাগবে 70 - 55 = 15 men.

২৪.
Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days ten adults left and four children joined them. How many days will they now take to complete the remaining work?
  1. ক
    ক) 3
  2. খ
    খ) 4
  3. গ
    গ) 6
  4. ঘ
    ঘ) 8
ব্যাখ্যা

1 child's 1 day's work = 1/192;
1 adults 1 day's work = 1/96.
Work done in 3 days = (1/96) × 16 × 3
= 1/2
Remaining work = {1 - (1/2)}
= 1/2.
(6 adults + 4 Children)'s 1 day's work = (6/96) + (4/192)
= 1/12
1/12 work is done by them in 1 days
1/2 work is done by them in (12 × (1/2)}
= 6 days.