Bank Math Master

Question: A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 10%. The percentage of water in the mixture is-

Solution:
Let,
the cost price = 100
selling price = 110

So the amount of milk = 100/110
= 10/11

∴ Amount of water = (1 - 10/11) × 100%
= 9.09%

Question: There are Tiger and peacock in zoo. The total number of their heads is 60 and the total number of their legs is 180. How many peacocks are there?

Solution:
Let,
There are x peacocks

So the number of tiger = (60 - x)

ATQ,
2x + 4(60 - x) = 180
⇒ 2x + 240 - 4x = 180
⇒ 240 - 2x = 180
⇒ 240 - 180 = 2x
⇒ 60 = 2x
⇒ x = 60/2
∴ x = 30

Question: A train running at the speed of 66 km/h crosses a pole in 15 seconds. What is the length of the train?

Solution:
Given,
Speed = 66 km/h
= (66 × 5/18) m/sec
= 55/3 m/sec

So the length of the train = (55/3 × 15) m
= 275 m

Question: The speed of A and B are in the ratio 4 : 7. B takes 21 minutes less than A to reach a destination. Time in which B reach the destination?

Solution:
Given
The speed of A and B are in the ratio = 4 : 7

So the ratio of time taken = 7 : 4  [As Speed ∝ 1/Time, When distance remains constant.]

Let,
time taken by A and B be 7x and 4x minutes respectively.

ATQ,
7x - 4x = 21
⇒ 3x = 21
∴ x = 7

Hence, time taken by B = (4 × 7) minutes
= 28 minutes

Question: 800 grams of sugar solution has 40% sugar in it. How much sugar should be added to make 60% in the solution? 

Solution:
Amount of sugar = 800 × 40/100
= 320 grams

Let,
x gm sugar to be added

ATQ,
(320 + x)/(800 + x) = 60%
⇒ (320 + x)/(800 + x) = 3/5
⇒ 1600 + 5x = 2400 + 3x
⇒ 5x - 3x = 2400 - 1600
⇒ 2x = 800
∴ x = 400

Question: A train passes a station platform in 36 seconds and a man standing on the platform in 15 seconds. If the speed of the train is 90 km/h, what is the length of the platform?

Solution:
Given,
Speed of the train = 90 km/h
= (90 × 5/18) m/sec
= 25 m/sec

Length of the train = (25 x 15) m
= 375 m

Let,
The length of the platform = x metres.

ATQ,
(x + 375)/36 = 25
⇒ x + 375 = 900
⇒ x = 900 - 375
∴ x = 525 m

Question: A mixture contains 1/5 of element A and 4/5 of element B. When 5 ml of A is added to the mixture, the proportion of B in the mixture changes to 1/5. What amount of A was originally present in the mixture before the addition was made?

Solution: 
Let,
Mixture be x ml.
A = x/5 ml
B = 4x/5 ml

After adding 5 ml of A to mixture, amount of B remained same.
And the mixure be x + 5 ml.
New
B = (x + 5)/5

Now,
(4x)/5 = (x + 5)/5
⇒ 20x = 5x + 25
⇒ 15x = 25
⇒ x = 25/15
∴ x = 5/3

Original amount of A = (5/3)/5 ml
= 1/3 ml

Question: In a race of 200 meters, B can gives a start of 20 meters to A, and C can gives a start of 30 meters to B. The starts that C can gives to A, in the same race is-

Solution:
According to question,
When B runs 200 m meters, A runs 180 meters;
Hence, when B runs 170 meters,
A runs = (180 × 170)/200
= 153 meters

When C runs 200m, B runs 170 meters.
Hence,
C will give a start to A by = (200 - 153) meters
= 47 meters

Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes. How long will it take to go 9 km in stationary water?

Solution:
Rate downstream = (1/15 × 60) km/h
= 4 km/h

Rate upstream = 2 km/h

Speed in still water = (4 + 2)/2 km/h
= 3 km/h

Required time = (9/3) h
= 3 h

সঠিক উত্তর: 252 liters
অপশনে সঠিক উত্তর না থাকায় প্রশ্নটি বাতিল করা হলো। 
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Question: A 180 liter mixture of milk and water contains 30% water. How much milk, in liters must be added to the mixture will contain water and milk in the ratio of 1:7?

Solution:
Milk = 180 × (100 -30)%
= 180 × 70%
= 180 × (70/100)
= 126

Remaining = 180 - 126 = 54 liters

Let,
x liter milk has to added

ATQ,
54 : (126 + x) = 1 : 7
⇒ 54/(126 + x) = 1/7
⇒ 378 = 126 + x
⇒ x = 378 - 126
∴ x = 252 liters

Question: A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 50 meters, and the speed of the train is 45 km/hr. In 4 hours, how many pillars will he count?

Solution:
Distance covered by the train in 4 hours = (Speed × Time)
= (45 × 4) km
= 180 km
= 180000 m

∴ Number of pillars counted by the man = (180000/50) + 1
= (3600 + 1)
= 3601

Question: The speed of a boat in still water in 12 km/h and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is-

Solution:
Speed downstream
= (12 + 3) kmph
= 15 kmph

Distance travelled = (15 × 24/60) km
= 6 km

Question: Two equal glasses are respectively two-third and three-fourth full of milk. They are then filled up with water and the contents are mixed in a tumbler. Ratio of milk and water in tumbler is 

Solution:
In 1st glass milk = 2/3
Water = (1 - 2/3)
= 1/3

In 2nd glass milk = 3/4
Water = (1 - 3/4)
= 1/4

Ratio of milk and water = (2/3 + 3/4) : (1/3 + 1/4)
= {(8 + 9)/12} : {(4 + 3)/12}
= (17/12) : (7/12)
= 17 : 7

Question: A man can row at 8 kmph in still water. If the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back, how far is the place?

Solution:
Speed downstream = (8 + 2) kmph = 10 kmph
Speed upstream = (8 - 2) kmph = 6 kmph
Let the required distance be x km

ATQ,
(x/10) + (x/6) = 2
⇒ (3x + 5x)/30 = 2
⇒ 8x = 60
∴ x = 7.5

Question: To gain 25% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is:

Solution:
Let the quantity of water mixed be x kg
Let CP of 1 kg of pure milk = Tk 1

Hence,
% gain = x × (100/50)
⇒ 25 = 100x/50
⇒ 100x = 1250
∴ x = 12.5

Question: Two buses start from a bus terminal with a speed of 30 km/h at interval of 15 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at interval of 10 minutes?

Solution:
Let Speed of the man is x kmph.

Let the speed of the man be x km/h
Distance covered by the man in 10 min = Distance covered by the bus in 5 min

According to the question
⇒ x × 10/60 = 30 × 5/60
⇒ 10x = 150 ⇒
x = 15 km/h

∴ Speed of the man is 15 km/h

Question: A merchant has 100 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is-

Solution:
By the rule of alligation, we have:

⇒ Quantity of cheaper : Quantity of Dearer = (CP of of Dearer - Mean Price) : (Mean Price - CP of Cheaper)
⇒ Quantity of cheaper : Quantity of Dearer = (18-14) : (14-8)
= 4 : 6
= 2 : 3

∴ Quantity of 2nd kind = (3/5 × 100) kg
= 60 kg

Question: A man covers half of his journey at 12 km/h and the remaining half at 6 km/h. His average speed is-

Solution:
Given,
Man covers half of his journey at 12 km/h
The remaining half at 6 km/h

His average speed is = (2 × 12 × 6)/(12 + 6)
= 144/18
= 8 km/h