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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes
মোট প্রশ্ন১৭
সিলেবাস
Time & Work, Pipes & Cisterns [ব্যাংকের সকল পরীক্ষা যেকোনো প্যাকেজের জন্য ফ্রি]
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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ১৭ প্রশ্ন

১.
A full tank gets emptied in 8 minutes due to the presence of a leak in it. On opening a tap which can fill the tank at the rate of 9 L/min, the tank gets emptied in 12 min. Find the capacity of a tank?
  1. ক
    ক) 180 L
  2. খ
    খ) 240 L
  3. গ
    গ) 216 L
  4. ঘ
    ঘ) 204 L
ব্যাখ্যা

a = 8; b = 9; C = 12
Capacity of a tank
= a × b × c/(c-a)
= (8 × 9 × 12)/4
= 216 Litre.

২.
A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
  1. ক
    ক) 40
  2. খ
    খ) 80
  3. গ
    গ) 54
  4. ঘ
    ঘ) 60
ব্যাখ্যা

(A +B)'s 20 day's work = 20 × 1/30 = 2/3
Remaining work = 1 − 2/3 = 1/3
Now,1/ 3 work is done by A in 20 days
∴ The whole work will be done by A
in 20×3 = 60days

৩.
Pipe A can fill the tank in 8 hours and pipe B can fill it in 12 hours. If pipe A is opened at 7:00 AM and pipe B is opened at 9:00 AM, then at what time will the tank be full ?
  1. ক
    ক) 12:10 PM
  2. খ
    খ) 12:30 PM
  3. গ
    গ) 11:48 PM
  4. ঘ
    ঘ) 12:36 PM
ব্যাখ্যা

A opened 2 hours early to B
In 2 hours A can do 3 × 2 = 6 unit work
Remaining work = 24 - 6 = 18
A + B can do it in
= 18/5 hours
= 3 hours 36 minutes
∴ Tank will be full in 9 A.M. + 3 hours 36 minutes = 12.36 P.M.

৪.
Two pipes A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C are open together to fill the tank in 15 minutes, find the capacity of the tank?
  1. ক
    ক) 160 gallons
  2. খ
    খ) 150 gallons
  3. গ
    গ) 120 gallons
  4. ঘ
    ঘ) 60 gallons
ব্যাখ্যা

Work done by the C pipe in 1 minute
= 1/15 − (1/20 + 1/24)
= (1/15 − 11/120)
= −1/40 [−ve means emptying]
∴ Volume of 1/ 40 part = 3 gallons.
Volume of whole = (3 × 40) gallons = 120 gallons.

৫.
3/ 4 part of the tank is full of water. When 30 litres of water is taken out, the tank becomes empty. The capacity of the tank is -
  1. ক
    ক) 32 liters
  2. খ
    খ) 42 liters
  3. গ
    গ) 40 liters
  4. ঘ
    ঘ) 38 liters
ব্যাখ্যা

If a tank has 4x liters of total capacity and it holds 3x liters of water and if 30 liters of water is taken out, the tank becomes empty.
It means 3x liters of water is taken out
3x = 30 liters
x = 10 liters
Capacity of tank
= 4x = 4 × 10 = 40 liters

৬.
A pipe can fill a tank in x hours and another pipe can empty it in y (y > x) hours. If both pipes are open, in how many hours will the tank is filled?
  1. ক
    ক) (x - y) hours
  2. খ
    খ) (y - x) hours
  3. গ
    গ) xy/(x - y) hours
  4. ঘ
    ঘ) xy/(y - x) hours
ব্যাখ্যা

Net part filled in 1 hour
= (1/x − 1/y)
= (y−x)/xy
∴ The tank will be filled in
= xy/(y−x) hours

৭.
12 pumps working 6 hours a day can empty a completely filled reservoir in 15 days. How many such pumps working 9 hours a day will empty the same reservoir in 12 days?
  1. ক
    ক) 16
  2. খ
    খ) 9
  3. গ
    গ) 10
  4. ঘ
    ঘ) 12
ব্যাখ্যা

Apply formula of
M1D1H1/W1= M2D2H2/W2
Let 'P' pumps are required to empty the reservoir.
(12pumps×6hours×15days)/1 reservoir
= (P×9hours×12days)/1 reservoir
P = 10 pumps

৮.
Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
  1. ক
    ক) 5 hour
  2. খ
    খ) 2 hours
  3. গ
    গ) 6 hours
  4. ঘ
    ঘ) 8 hours
ব্যাখ্যা

Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours
∴ 1/ x + 1/ x+6 = 1/ 4
⇒ x+6+x/ x(x+6) = 1/ 4
⇒ x² − 2x−24 = 0
⇒ (x−6)(x+4) = 0
⇒ x = 6 [neglecting the negative value of x].

৯.
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
  1. ক
    ক) 22 hours
  2. খ
    খ) 26 hours
  3. গ
    গ) 35 hours
  4. ঘ
    ঘ) Cannot be determined
ব্যাখ্যা

Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
∴ 1/x + 2/x + 4/x = 1/5
⇒ 7/x = 1/5
⇒ x = 35 hours

১০.
Having the same capacity 9 taps fill up a water tank in 20 minutes. How many taps of the same capacity are required to fill up the same water tank in 15 minutes?
  1. ক
    ক) 8 taps
  2. খ
    খ) 12 taps
  3. গ
    গ) 15 taps
  4. ঘ
    ঘ) 18 taps
ব্যাখ্যা

(m1×h1×t1)/w1 = (m2×h2×t2)/w2
9 taps × 20 min = t taps × 15 min
So, t = 12 taps

১১.
A, B and C completed a work costing Tk. 1800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much amount will be received by A?
  1. ক
    ক) 600
  2. খ
    খ) 750
  3. গ
    গ) 800
  4. ঘ
    ঘ) 900
ব্যাখ্যা

Let the daily wages of A, B and C be Tk. 5x, Tk. 6x and Tk. 4x respectively.
Then, ratio of their amounts
= (5×6):(6×4):(4x9)
= 30:24:36
= 5:4:6
∴ A's amount
= Tk. (1800 × 5/15)
= Tk. 600

১২.
A can finish a piece of work in 18 days and B can do the same work in half of the time taken by A. Then working together what part of the same work they can finish in a day?
  1. ক
    ক) 1/6
  2. খ
    খ) 2/5
  3. গ
    গ) 1/9
  4. ঘ
    ঘ) 2/7
ব্যাখ্যা

A's 1 day work = 1/18
B's 1 day work = 1/9 [because B take half time than A]
So, (A + B)'s one day work
= 1/18 + 1/9
= (1+2)/18
= 1/6

১৩.
Two men can do a piece of work in x days. But y women can do that in 3 days. Then the ratio of the work done by 1 man and 1 woman is?
  1. ক
    ক) 3y : 2x
  2. খ
    খ) 2x : 3y
  3. গ
    গ) 2x : y
  4. ঘ
    ঘ) 2y : 3x
ব্যাখ্যা

2 men can do a work in x days
1 men can do a work in (2 × x) days
y women can do a work in 3 days
1 women can do a work in 3y days
1 man : 1 woman
Days - 2x : 3y
Efficiency - 3y : 2x

১৪.
The ratio of the amount of work done by (x-1) labours in (x+1) days and (x+1) labours in (x+2) days is 5 : 6. Then the value of x is?
  1. ক
    ক) 16
  2. খ
    খ) 20
  3. গ
    গ) 17
  4. ঘ
    ঘ) 15
ব্যাখ্যা

From M1D1 = M2D2
⇒ M1D1 / M2D2 = 5/6
⇒ (x−1)(x+1)/(x+1)(x+2) = 5/6
⇒ (x−1)/(x+2) = 5/6
⇒ 6x−6 = 5x+10
⇒ x = 16

১৫.
639 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 ?
  1. ক
    ক) 222 days
  2. খ
    খ) 213 days
  3. গ
    গ) 214 days
  4. ঘ
    ঘ) 215 days
ব্যাখ্যা

According to the question,
Let, D is number of days
(639×12×5)/1 road = (30×6×D)/1 road
⇒ D = 213 days

১৬.
A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
  1. ক
    ক) 4
  2. খ
    খ) 5.5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 8
ব্যাখ্যা

B's 10day's work = 1/15 × 10 = 2/3
Remaining work =
(1−2)/3 = 1/3
Now,
1/18 work is done by A in 1 day
∴ 1/3 work is done by A in 18 × 1/3 = 6 days

১৭.
Working 5 hours a day, A can complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in:
  1. ক
    ক) 3 days
  2. খ
    খ) 4 days
  3. গ
    গ) 4.5 days
  4. ঘ
    ঘ) 5.4 days
ব্যাখ্যা

Working 5 hours a day, A can complete the work in 8 days i.e.
= 5 × 8 = 40 hours
Working 6 hours a day, B can complete the work in 10 days i.e.
= 6 × 10 = 60 hours
(A + B)'s 1 hour's work,
= 1/40 + 1/60 = (3+2)/ 120
= 5/120
= 1/24
Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.