ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Income ratio = Ratul : Sajib = 5 : 6 = 5/6
Common factor helps in finding actual values easily
So, take 'A' as a common factor.
Income of Ratul = 5A; Income of Sajib = 6A
(Expenses of Ratul)/(Expenses of Sajib) = (Ratul Income - Ratul Saving)/(Sajib Income -Sajib Saving) = 7/9
Since Ratul save, Tk. 1000/- more than Sajib, Ratul's savings = Tk. 4000/-
5A - 4000/6A - 3000 = 7/9
∴ 9(5A-4000) = 7(6A-3000)
∴ A = 5000
Income of Ratul = 5A = 25000 ; Income of Sajib = 6A = 30000
Spending of Ratul =25000 - 4000 = 21000
Spending of Sajib = 30000 - 3000 = 27000.

B is common to both the ratios.
Values of b = 4 and 9 (That means they are not the same)
Make the values of 'b' the same as follows -
Multiply 3 : 4 up and down with 9 as shown
∴ (3 × 9)/(4 × 9) = 27/36 = a/b
Multiply 9 : 7 up and down with 4 as shown
∴ (9 × 4)/(7 × 4) = 36/28 = b/c
Since values of b are the same = 36
a : b : c = 27 : 36 : 28

Common factor helps in finding actual values easily
So, take 'A' as a common factor.
∴ 3 numbers will now be 42A, 32A and 23A
∴ 42A + 32A + 23 A = 3395
∴ 97A = 3395
∴ A = 35
3 parts of 3395 are
42A = 42 x 35 = 1470;
⇒ 32A = 32 x 35 = 1120
⇒ 23A = 23 x 35 = 805
These are the amounts to be paid.

The ratio of original money numbers = 3:8
Common factor helps in finding actual values easily
So, take 'M' as a common factor.
∴ Original numbers will be 3M and 8M
Adding 5 to them, we get (3M + 5) and (8M+5)
∴ (3M + 5)/(8M + 5) = 2/5 ............ (Ratio of new numbers is 2:5)
∴ 15M + 25 = 16M + 10
∴ M = 15
Smaller money value is 3M = 3 x 15 = 45.

Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x + 5) = 4/5
⇒ 20x = 4(3x + 5)
⇒ 8x = 20
⇒ x = 2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.

Let the number A, B and C be 12a , 15a and 25a respectively
Then from the question 12a + 15a + 25a = 312
⇒ 52a = 312
⇒ a = 312/52
⇒ a = 6
Required ratio = {(15 × 6) - (12 × 6)}/{(25 × 6) - (15 × 6)}
= 3/10
= 3 : 10.

The ratio of 1st and 2nd numbers = 3 : 4
The ratio of 2nd and 3rd numbers = 5 : 6
Let,
the 2nd number = 5x, third number = 6x
Product of 2nd and 3rd numbers = 4320
5x × 6x = 4320
x² = 144
x = 12
2nd number = 60, 3rd number = 72,
1st number = (60/4) × 3 = 45
Sum of three numbers = 60 + 72 + 45 = 177

Let the numbers be 21x and 26x.
⇒ (21x + 8)/(26x + 8) = 5/6
⇒ 6(21x + 8) = 5(26x + 8)
⇒ 126x + 48 = 130x + 40
⇒ x = 2.
So, the numbers will be 42 and 52.
If 6 is subtracted, then numbers will be 36 and 46.
Required ratio = 36 : 46.
i.e. 18 : 23.

Let the constant be x,
so putting the first scenario in equation
A = x × (B/C)
⇒ 6 = x × 2/3
⇒ 2x = 18
⇒ x = 9
We can find out A in the second scenario by putting the value of x as 9
A = 9 × 8/6
⇒ A = 12.

Income = Expenditure + Saving
Asim : 12x = 15y + 3x (3x = 25% of 12x)
Shakil : 9x = 9y + (9x – 9y)
Riaz : 7x = 8y + (7x – 8y)
Therefore, 12x – 3x = 15y
x/y = 5/3
y = 3x/5
Therefore, savings = (income – expenditure)
Asim = 12x – 9x = 3x
Shakil = 9x - 9y = 9x - (27x/5)
= 18x/5
Riaz = 7x - 8y = 7x - (24x/5)
= 11x/5
i.e., the ratio of savings of Asim : Shakil : Riaz
= 3x : 18x/5 : 11x/5
= 15 : 18 : 11.

We know,
The ratio of Investment x Time = Ratio of Profit
∴ (A's investment x Time) : (B's investment x Time) = Profit of A : Profit of B

∴ (Robi's Investment x Time) : (Rasel's Investment x Time) = Robi's Profit : Rasel's Profit
∴ 40000 x 12 : 50000 x 8 = Robi's Profit : Rasel's Profit
∴ Robi's Profit : Rasel's Profit = 4,80,000 : 4,00,000 = 6:5
∴ Rasel's profit = (5/11) × 187000 = Tk. 85000

We know that Ratio of Investment x Time = Ratio of Profit
∴ To find the ratio of time just divide respective profits ratios by respective investment ratios
So if the profit ratio is P₁: P₂ : P₃ and the investment ratio is I₁ : I₂ : I₃ then,
Time ratio is found by = (P₁/I₁) : (P₂/I₂) : (P₃/I₃)

6 : 4 : 10 can be reduced to 3 : 2 : 5. So, their investments are actually in the ratio 3 : 2 : 5.
The ratio of time periods for A, B, and C is found by = 8/3 : 7/2 : 9/5
Making denominators common by multiplying by 30
∴ The ratio of Time periods for A, B, and C = (30 × 8)/3 : (30 × 7)/2 : (30 × 9)/5
= 80 : 105 : 54

We know that
The ratio of Investment x Time = Ratio of Profit
∴ (A's investment × Time) : (B's investment × Time) = Profit of A : Profit of B

∴ Tk. 8000 × 12 months : Tk. 16000 × 9 months : Tk. 40000 × ? months = 6 : 9 : 5
∴ 96000 : 144000 : 40000 × ? = 6 : 9 : 5
By direct observation we can say, if common factor is K, then
6K = 96000;
∴ K = 16000;
and 5K = 40000 × ?
? = 5k/40000
= (5 × 16000)/40000
= 2 months.

The total value of investment of Roman and Shimul after 12 months is =
Tk. 35000 x 12 months : Tk. 25000 x 12 months = 420000 : 300000

Profits need to be the same so investment share must be the same too.

Now 400000 given by Salim needs to be shared by Roman and Shimul so that their investment value becomes the same.
∴ If Tk. X must be given to Roman,
Then,
420000 + X = 300000 + (400000-X)
∴ X = Tk. 140000 = Roman should get this much
Required ratio = Share of Roman: Share of Shimul
= 140000 : (400000 - 140000)
= 7 : 13.

Let investment of C be Tk. 100
So the investment of B = Three-fourths of C = 3/4 of Tk. 100 = Tk. 75
Investment of A = 20% more than B = 20% more than Tk. 75 = Tk. 90
Ratio of investment of A, B, and C = 90 : 75 : 100 = 18 : 15 : 20
Investment of C = 20/(18 + 15 + 20) × 3816
= Tk. 1440.

We know,
The ratio of Investment x Time = Ratio of Profit
∴ (A's investment x Time) : (B's investment x Time) = Profit of A : Profit of B

The total value of investment of Arman, Ghalib, and Jishan after 12 months is =
Tk. 40000 x 12 months : Tk. 80000 x 7 months : Tk. 144000 x (12 - 7)months = 480000 : 560000 : 720000
∴ Profit ratio = 240000 : 280000 : 360000 = 6 : 7 : 9
∴ Share of Ghalib = 7/(6 + 7 + 9) x 50600 = Tk. 16100

Suppose B invested Tk. x for y months.
Then, A invested Tk. 3x for 2y months.

So,
A : B = (3x × 2y) : (x × y)
= 6xy : xy
= 6 : 1.
B's profit : Total profit = 1 : 7.

Let the total profit be Tk. x
Then, 1/7 = 4000/x
⇒ x = Tk. 28000.

Let money invested by Rubel = Tk. x
Money invested by Tushar = 9/10 x = 0.9x
Money invested by Himu = 9/10x × 110/100 = 0.99x
Also, x + 0.9x + 0.99x = 5780
= x= 5780/2.89
= 2000

Therefore, amount invested by Rubel is Tk. 2000.

A : C = 2 : 3 or 2x : 3x
B : D = 1 : 2 or y : 2y
According to question,
2x - 140 = y .... (i)
3x - 80 = 2y .... (ii)

multiply equation (i) by 2 and solved
4x - 280 - 3x + 80 = 2y - 2y
⇒ x - 200 = 0
⇒ x = 200

Now put value of x in equation (i)
(2 × 200) - 140 = y
⇒ 400 - 140 = y
⇒ y = 260

A's salary = 2x = Tk. 400
B's salary = y = Tk. 260
C's salary = 3x = Tk. 600
D's Salary = 2y = Tk. 520

Current alcohol quantity = {(45/100) × 80}
= 36 Litres.

Let A be alcohol added.
So, 36 + A = (75/100) × (80 + A)
⇒ 36 + A = (3/4) × (80 + A)
⇒ 144 + 4A = 240 + 3A
∴ A = 96 Litres =

96 Litres is the additional quantity of alcohol to be added.

First 4L orange juice was removed
So now in 40L mixture, there is 40 - 4 = 36 litres orange juice and 4 litres water
Now, remove 4L mixture. While doing this proportionate amount of juice and water gets removed.
Amount of juice removed = 4 × (Juice quantity/Mixture quantity)
= 4 × (36/40)
= 3.6 Litres.

Orange Juice remaining = 36-3.6 = 32.4 Litres
Again 4L mixture removed
Amount of juice removed = 4 × (Juice quantity/Mixture quantity)
= 4 × (32.4/40)
= 3.24 Litres.

Juice remaining = 32.4 - 3.24
= 29.16 Litres.

Children's drink → Juice : Water = 5 : 2 → Total 5 + 2 = 7 parts of liquid
Adult's drink → Juice : Water = 7 : 4 → Total 7 + 4 = 11 parts of liquid

Jug juice = Juice from children's mix + juice from adult mix = 5/7 + 7/11
= 104/77
Jug Water = Water from children's mix + Water from adult's mix = 2/7 + 4/11
= 50/77

Water to juice ratio in Jug = 50/77 : 104/77
= 50 : 104
= 25 : 52

3 vessels of 30 litres each = 3 X 30 = 90 ml milk mixture
Amount of milk in mixture = 2/(2 + 1) × 90 = 60L
Amount of water = 90 - 60 = 30L

To make milk to water ratio 1 : 2, we simply need to make water double of milk.
By direct observation,
we can say that we should have 60L x 2 = 120L water to make the required ratio

We already have 30L,
we need (120 - 30) = 90L more water.

Let the rate of 3^rd type of wheat be Tk. W
Quantity ratio = 2 : 1 : 3
This means if we take 2kg of Type 1 and 1 kg of Type 2, then we must take 3kg of Type 3.
Also, the mix will have 2kg + 1kg + 3kg = 6 kg quantity.
∴ (145 x 2) + (165 x 1) + (3 x W) = 6 x 180
⇒ 290 + 165 + 3W = 1080
⇒ 3W = 1080 - 455
⇒ 3W = 625
⇒ W = 625/3
⇒ W = 208.33

∴ W = Tk. 208.33 per kg = 3^rd type price per kg

Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively
Quantity of A in mixture left = {7x - (7/12) × 9} = 7x - 21/4
Quantity of B in mixture left = {5x - (5/12) × 9} = 5x - 15/4

According to the question,
(7x - 21/4)/{(5x - 15/4) + 9} = 7/9
⇒ (28x - 21)/(20x + 21) = 7/9
⇒ 252x - 189 = 140x + 147
⇒ 252x - 140x = 147 + 189
⇒ 112x = 336
⇒ x = 3.

So, they can contain 21 litres of A.

Number of liters of water in 125 liters of the mixture = 20% of 150
= 1/5 of 150
= 30 liters

Let us Assume that another 'P' litres of water is added to the mixture to make water 25% of the new mixture.
So, the total amount of water becomes (30 + P) and the total volume of the mixture becomes (150 + P).

Thus, (30 + P) = 25% of (150 + P)
⇒ 30 + P = 25/100 of (150 + P)
⇒ 30 + P = (1/4) × (150 + P)
⇒ 120 + 4P = 150 + P
⇒ 4P - P = 150 - 120
⇒ 3P = 30
⇒ P = 10

10 Litres of water is added to the mixture to make water 25% of the new mixture.

Copper in 4 kg = 4/5 kg and
Zinc in 4 kg = 4 x (4/5) kg

Copper in 5 kg = 5/6 kg and
Zinc in 5 kg = 5 x (5/6) kg

Therefore, Copper in mixture = (4/5) + (5/6) = 49/30 kg
and Zinc in the mixture = (16/5) + (25/6) = 221/30 kg

Therefore the required ratio = 49/30 : 221/30
= 49 : 221.

Let the milk he bought is 1000 ml
Let C.P of 1000 ml is Tk. 100

Here let he is mixing K ml of water
He is getting 30% profit

⇒ Now, the selling price is also Tk. 100 for 1000 ml
⇒ 100 : K%
⇒ 100 : 30
10 : 3 is the ratio of milk to water

Percentage of milk = 10 x 100/13
= 1000/13
= 76.92%

Let us assume that the lotion has 50% alcohol and 50% water.
ratio = 1:1
As the total solution is 9ml
alcohol = water = 4.5ml
Now if we want the quantity of alcohol = 30%
The quantity of water = 70%
The new ratio = 3:7

Let x ml of water be added
We get,
4.5/(4.5 + x) = 3/7
⇒ 9/(9 + 2x) = 3/7
⇒ 63 = 27 + 6x
⇒ 6x = 63 - 27
⇒ 6x = 36
⇒ x = 6

Hence 6ml of water is added.