Bank Math Master

Question: There are peacock and horse in a zoo. The total number of their heads is 50 and the number of legs is 140. How many horses are there?

Solution:
Let, there are x horses.

ATQ,
4x + (50 - x)2 = 140
4x + 100 - 2x = 140
2x = 40
x = 20

Question: A man covers half of his journey at 10 km/h and the remaining half at 4 km/h. His average speed is:
Solution:
let, the total road is 2x
first x distance is covered in 10 km/h
∴ time = x/10 h
second x distance is covered in 4 km/h
∴time = x/4 h

∴ average speed is = total distance/ total time
= 2x / (x/10 + x/4)
= 2x / (7x/20)
= 40/7
= 5.71 km/h

Question: A dishonest milkman professes to sell his milk at cost price but he mixes water with it and thereby gains 20%. The percentage of water in the mixture is:

Solution:
let, 
cost price = 100
sell price = 120

∴ the amount of milk = 100/120
= 5/6

∴ the amount of water is = (1 - 5/6) × 100%
= 16.67%

Question: In a 100m race, Rakib defeats Tanvir by 5 seconds. If the speed of Rakib is 18 kmph, then the speed of Tanvir is:
Solution:
Hints: (km/h)/3.6 = m/s
Time taken by Rakib = 100 / (18/3.6) seconds
= 20 seconds

Hence,
Time taken by Tanvir is = 20 + 5 = 25 seconds
So, Tanvir's speed=100/25 m/s
= 4 m/s
= 4 × 3.6 km/h
=14.4 km/h

Question: Two equal glasses respectively contain one-fourth and two-fifth of milk. What is the ratio of milk and water if the rest of the glasses are filled with water and then mixed in a tumbler?

Solution: 
in the first glass,
milk = 1/4
water = 1 - (1/4) 
= 3/4

in the second glass,
milk = 2/5
water = 1 - (2/5)
= 3/5

so, 
milk : water 
(1/4 + 2/5) : (3/4 + 3/5)
(5+8)/20 : (15+12)/20
13 : 27

Question: A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is:

Solution: 
Let the speed of the train is x km/h

As the man was running in the same direction, 
the resultant speed is = train - man
= x - 5 km/h
= (x - 5)/3.6 m/s

ATQ,
time = distance/speed
20 = 250/((x-5)/3.6)
20x - 100 = 900
x = 50 km/h

Question: In what ratio water must be mixed with milk costing Tk. 50 per liter to get a mixture worth Tk. 35 per liter?

Solution:
Cost Price of water Tk. 0
Cost Price of milk TK. 50
Mean Price of mixure Tk. 35
Let,
Quantity of water be x
Quantity of milk be y
Using the formula,

x/y = (50-35)/(35-0)
x/y = 15/35
x/y = 3/7
∴x : y = 3 : 7

Question: The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream at the same time, the speed of the stream is-

Solution: 
Let the speed of the stream be x km/hr
Then speed downstream = (10 + x) km/hr
Speed upstream = (10 − x)km/hr

∴26/(10 + x) = 14/(10 − x)
⇒ 260 − 26x = 140 + 14x
⇒ 40x = 120
⇒ x = 3 km/hr

Question: The ratio between the speeds of a bus and bike is 5 : 8. If the bus travels 120 km in 2 hours, find the speed of the
bike.
Solution:
Let,
the speed of bus and bike is 5X and 8X.
Speed of bus = 120/2 = 60 km/hr
So, 5X= 60
.. X = 60/5
= 12 km/hr

Speed of bike = 8X
= 8 × 12
= 96 km/hr

Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

Solution: 
Let the length of the train is x m
speed = 72 kmph
= 72/3.6 mps
= 20 mps

As we know,
Distance = Speed × Time
x + 250 = 20 × 26
x = 520 - 250
x = 270 m 

Question: The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. Time in which A reach the destination?
Solution: 
here, ratio of speed is 3 : 4
as the ratio of time is inversly proportional to speed,
ratio of time = 4 : 3

ATQ,
4x - 3x = 20 min
x = 20 min = 1/3 hr

A takes total time of = 4 × 1/3 = 4/3 hr

Question: A mixture of 200 liters of wine and water contains 30% water. How much more water should be added so that water becomes 40% of the new mixture?

Solution:
Number of liters of water in 200 liters of the mixture = 30% of 200 = 30/100 × 200 = 60 liters.

Let P liters of water added to the mixture to make water 25% of the new mixture.

Total amount of water becomes (60 + P) and total volume of mixture is (200 + P).
(60 + P) = 40/100 × (200 + P)
300 + 5P = 400 + 2P
=> P = 33.33 liters.

Question: A boat goes 15 km downstream in 45 minutes. The speed of stream is 3km/hr. The speed of boat in still water is-

Solution: 
স্রোতের প্রতিকূলে 45 মিনিটে যায় 15 কি.মি.
স্রোতের প্রতিকূলে 1 মিনিটে যায় 15/45 কি.মি.
স্রোতের প্রতিকূলে 1 ঘণ্টা বা 60 মিনিটে যায় (15 × 60)/45 কি.মি./ঘণ্টা
= 20 কি.মি./ঘণ্টা

স্রোতের বেগ = 3 কি.মি./ঘণ্টা
স্থির পানিতে নৌকার বেগ = (20 - 3) কি.মি./ঘণ্টা
= 17 কি.মি./ঘণ্টা

Question: Salman is traveling in a constant velocity. The time ratio that he needs to pass the distances of 300 km and 500 km is:

Solution: 
if the velocity or speed remain the same,
time is proportional to distance.

∴ t₁ : t₂ = 300 : 500
t₁ : t₂ = 3 : 5

Question: The price of a variety of a commodity is Tk. 7 per kg and that of another is Tk. 12 per kg. Find the ratio in which two varieties should be mixed so that the price of the mixture is Tk. 10 per kg.

Solution:
Let the mixed amount of the first and second commodity is A and B

∴ A : B = (12-10) : (10-7)
A : B = 2 : 3

Question: Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. The speed of the current is?

Solution: 
Let the speed of the boat is S
the speed of the current is W

S + W = 14 . . . . . . (i)
S - W = 8 . . . . . . . .(ii)
_________________
from equation (i) & (ii)
S = 11 km/hr, W = 3 km/hr
Speed of current = 3 km/hr

Question: A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is :

Solution: 
Let the original speed be S₁ and time t₁ and distance be D.
Now,
(D/2)/2t₁=S₂
S₂ = D/4t₁ and, S₁ = D/t₁

Thus,
S1_/S₂ = 4/1
= 4 : 1

Question: In a mixture of 35 liters, milk and water are in the ratio of 3:4. How much milk would be added to the mixture to make the ratio equal?

Solution: 
amount of milk
= (3/7)*35
= 15 litres
amount of water
= (4/7)*35
= 20 litres

the amount of milk to be added is
= (20-15)
= 5 litres.

Question: A boat goes 10km in one hour along the stream and 4 km in one hour against the stream. What is the speed of the boat?
Solution:
Let,
boat speed is x
stream speed is y

∴ x+y = 10
and, x-y = 4
so,
x+y+x-y = 10+4
2x = 14
x = 7