ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: In a bag, there are three types of coins- 1-tk, 50 paise and 25-paise in the ratio of 3 : 8 : 20. Their total value is 372. The total number of coins is

Solution:
Ratio of the number of coins of Re. 1, 50 paise and 25 paise = 3 : 8 : 20
Ratio of the values of these coins = 3 : (8/2) : (20/4) = 3 : 4 : 5

Value of 1 tk coins = (3/12) × 372 = 93 tk
Value of 50 paise coins = (4/12) × 372 = 124 tk
Value of 25 paise coins = (5/12) × 372 = 155 tk

Number of coins = 93 + (124 × 2) + (155 × 4)
= 93 + 248 + 620
= 961

Question: 1740 is divided among A, B, and C such that 0.5 of A = 0.6 of B = 0.75 of C. Then C will get

Solution:
A × 0.5 = B × 0.6 = C × 0.75
⇒ (A × 5)/10 = (B × 6)/10 = (C × 75)/100
⇒ A/2 = B/(5/3) = C/(4/3)
⇒ A : B : C = 2 : (5/3) : (4/3)
⇒ A : B : C = 6 : 5 : 4

∴ C’s share = (4/15) × 1740 = 464 tk

Question: A 24 liters of milk and water mixture contains milk and water in the ratio 3: 5. What litres of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?

Solution:
In 24 l of mixture, milk = (3/8) × 24 = 9 L
So water = 24 - 9 = 15 L
Now since the mixture is to be replaced with pure milk, the amount of mixture will remain same after replacement too.
In 24 L mixture, to have 12 L water and 12 L milk, 3 L of water should be taken out, since we are only adding milk.
Let x L of mixture taken out.
So (5/8) × x = 3
⇒ 5x = 24
Solve, x = 24/5 L

Question: In order to obtain an income of Tk. 720 from 8% stock at Tk. 90, one must make an investment of-

Solution:
To obtain Tk. 8, investment = Tk. 90.
To obtain Tk. 720
investment = Tk. (90/8) × 720
= Tk. 8100

Question: The salaries of P, Q, and R are in the ratio 5 : 8 : 6 and their expenses are in the ratio 4 : 7 : 5. If P saves 1/3rd of his salary then the savings of P, Q, and R are in the ratio of-

Solution:
Let the salaries of P, Q and R are 5x, 8x, and 6x respectively
and expenses of P, Q and R are 4y, 7y and 5y respectively
ATQ,
5x - 4y = 5x × 1/3
⇒ 15x - 12y = 5x
⇒ 10x = 12y
⇒ x : y = 12 : 10

∴ The ratio of savings of P, Q, and R
= (5x - 4y) : (8x - 7y) : (6x - 5y)
= (5 × 12 - 4 × 10) : (8 × 12 - 7 × 10) : (6 × 12 - 5 × 10)
= (60 - 40) : (96 - 70) : (72 - 50)
= 20 : 26 : 22
= 10 : 13 : 11
Therefore, the savings of P, Q, and R are in the ratio 10 : 13 : 11

Question: A and B enter into a partnership. A invest Tk 5000. At the end of 3 months, he withdraws Tk 500 and at the end of 7 months he withdraws another Tk 900. B gets Tk 800 as his share of the total profit of Tk 1800 at the end of the year. How much did B invest, if B invested along with A at the beginning of the year?

Solution:
A invest 5000 for 3 months, 4500 for 4 months and 3600 for 5 months and gets a interest of 1000

ATQ,
{(5000 × R × 3)/(12 × 100)} + {(4500 × R × 4)/(12 × 100)} + {(3600 × R × 5)/(12 × 100)} = 1000
⇒ {(15000 × R)/(12 × 100)} + {(18000 × R)/(12 × 100)} + {(18000 × R)/(12 × 100)} = 1000
⇒ (15000R/1200) + (18000R/1200) + (18000R/1200) = 1000
⇒  (51000R)/1200 = 1000
⇒ 51000R = 1200000
⇒ R = 1200000/51000
⇒  R=1200/51

For B,
{(P × 1200)/(51 × 1)}/100 = 800
⇒ (P × 1200/51)/100 = 800
⇒ (P × 1200)/51 = 80000
⇒  P × 1200 = 4080000
∴ P = 3400

Questions: An amount of money is to be distributed among P, Q and R in the ratio of 2 : 7 : 9. The total of P’s and Q’s share is equal to R’s share. What is the difference between the shares of P and Q?

Solution:
Let the amount to be distributed be Tk x.
P : Q : R = 2 : 7 : 9
Sum of the ratios = 2 + 7 + 9 = 18

P = (2/18) × x = x/9
Q = 7x/18
R = 9x/18 = x/2

As given, (x/9) + (7x/18) = (x/2)
⇒ (2x + 3x)/18 = (x/2)
⇒ x/2 = x/2
Thus, we get no conclusion. Amount should necessarily be known.

Question: The ratio of two positive numbers is 3 : 4. The sum of their squares is 400. What is the sum of the numbers?

Solution:
Let two positive numbers be 3x and 4x.
ATQ,
(3x)² + (4x)² = 400
⇒ 9x² + 16x² = 400
⇒ 25x² = 400
⇒ x² = 400/25
⇒ x² = 16
∴ x = 4

Sum of numbers = (3 × 4) + (4 × 4) = 28

Question: A, B and C enter into a partnership investing Tk 35000, Tk 45000 and Tk 55000 resp. The respective share of A, B and C in an annual profit of Tk 40500 are.

Solution:
A : B : C = 35000 : 45000 : 55000
= 7 : 9 : 11
Now, we are having the ratio. to get the share, first make total of above ratio. then get each share.

A's Share = 40500 × (7/27) = Tk. 10500
B's Share = 40500 × (9/27) = Tk. 13500
C's Share = 40500 × (11/27) = Tk. 16500

Question: The cost of variety A wheat flour is Tk. 42 per kg and variety B wheat flour is Tk. 35 per kg. If both variety A and variety B are mixed in the ratio of 3 : 2, then the price per kg of the mixed variety of wheat flour is:

Solution:
Let,
Quantity of variety A flour is 3x kg.
Quantity of variety B flour is 2x kg.
The price per kg of the mixed variety of flour is y taka
∴ Total price of variety A flour is 42 × 3x = 126x Taka
∴ Total price of variety B flour is 35 × 2x = 70x Taka

ATQ,
126x + 70x = y(3x + 2x)
⇒ 196x = y × 5x
⇒ y = (196x)/(5x)
∴ y = 39.2
Therefore, the price per kg of the mixed variety of wheat flour is Tk. 39.20

Question: By investing in (40/5)% stock at Tk. 72, one earns Tk. 1800. The investment made is:

Solution:
To earn Tk. 40/5, investment = Tk. 72
To earn Tk. 1, investment = Tk. 72 × (5/40)
To earn Tk. 1800, investment = Tk. {72 × (5/40) × 1800}
= Tk. 16200

Question: Solution A is made up of alcohol and water mixed in the ratio of 21 : 4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2 : 3 by volume. If Solution A and Solution B are mixed in the ratio of 5 : 6 by volume, what percent of the resultant mixture is alcohol?

Solution:
25 units of A contain 21 units of alcohol and 4 units of water.
So, 5 units of A contain (21/5) units of alcohol and (4/5) units of water
5 units of B contain 2 units of alcohol and 3 units of water

If we mix 5 × 5 = 25 units of A with 5 × 6 = 30 units of B (so that A and B are mixed in the ratio of 5 : 6), the resultant 55 units solution will contain:
Alcohol: (21/5) × 5 + (2 × 6) = 33 units
Water: (4/5) × 5 + (3 × 6) = 22 units

% of alcohol in the resultant solution = (33/55) × 100 = 60

Question: X and Y invest in business in the ratio 5 : 3. If 8% of the total profit goes to charity and X's share is Tk. 1380, the total profit is:

Solution:
Let the total profit be Tk. 100.
After paying to charity, X's share = (92 × 5/8) = 57.5
If X's share is Tk. 57.5, total profit = 100.
If X's share is Tk. 1380, total profit = (100/57.5 × 1380)
= 2400.
Therefore, the total profit is Tk. 2400.

Question: The ratio, by weight, of the four ingredients A, B, C, and D of a certain mixture is 4 : 7 : 8 : 12. The mixture will be changed so that the ratio of A to C is quadrupled and the ratio of A to D is decreased. The ratio of A to B will be held constant. If B will constitute 20% of the weight of the new mixture, by approximately what percent will the ratio of A to D be decreased?

Solution:
Lets say our thing has the weight x(4 + 7 + 8 + 12) = 31x.
When we change mixture our weight changes to x(4 + 7 + 2 + 12y)
=13x + 12xy

We also know that 7x = 0.2(13x + 12xy)
Reduce that last equation by x and lets just solve it for y : y = {7 - (0.2 × 13)}/2.4
= 11/6
So the original ratio was 4/12 = 1/3
The new ratio is (1 × 6)/(3 × 11) = 2/11
The resulting percentages are: {(1/3) - (2/11)}/(1/3) = 1 - (6/11)
= 5/11
= 0.4545
≈ 45%

Question: The market value of a 10.5% stock, in which an income of Tk. 756 is derived by investing Tk. 9000, brokerage being (1/4)% is -

Solution:
For an income of Tk. 756, investment = Tk. 9000
For an income of Tk. (21/2), investment = Tk. {(9000/756) × (21/2)}
= Tk. 125
∴ For a Tk. 100 stock, investment = Tk. 125
The market value of Tk. 100 stock = Tk. {125 - (1/4)}
= Tk. 124.75

Question: Consider three mixtures- the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has

Solution:
Mixtures A, B, & C are mixed in the ratio 4 : 3 : 2
Let the volumes = 4k, 3k, 2k respectively

Assume k = 60 [LCM(3, 4 & 5) = 60]
Volume of Liquid A = 8k/3 = 160
Volume of Liquid B = 9k/4 = 135
Volume of Liquid C = 8k/5 = 96
Volume of water = (4k/3) + (3k/4) + (2k/5)
= 80 + 45 + 24
= 149

There is more water than Liquid B

Question: P starts a business with Tk 6000 and after 3 months, Q joins with P as his partner. After a year, the profit is divided in the ratio 4 : 5. What is Q's contribution in the capital?

Solution:
Let Q's capital be Tk x
∴ P's share in 12 months = 6000 × 12
And, Q's share in 9 months = 9x
Then,
(6000 × 12)/(9x) = 4/5
⇒ 72000/9x = 4/5
⇒ 72000 = 36x/5
⇒ 72000 × 5 = 36x
⇒ 360000 = 36x
⇒ x = 10000

Question: How much must 1 pay for Tk. 1365 stock at 104? (brokerage 1%)

Solution:
Required answer = Tk. 1365 × (104 + 1)/100
= Tk. (1365 × 105)/100
= Tk. 1433.25

Question: In an innings of a cricket match, three players A, B and C scored a total of 361 runs. If the ratio of the number of runs scored by A to that scored by B and also number of runs scored by B to that scored by C be 3 : 2, the number of runs scored by A was-

Solution:
A : B = 3 : 2
B : C = 3 : 2
= {3 × (2/3)} : {2 × (2/3)}
= 2 : (4/3)

A : B : C = 3 : 2 : (4/3)
= 9 : 6 : 4

∴ A's share = 361 × (9/19)
= 171

Question: Rahim, Sohel and Tarek invested Tk.12000, Tk.9000 and Tk.15000 respectively in a business. Sohel left after four months. If after nine months, there was a gain of Tk.6975, then what will be the share of Tarek in this gain?

Solution:
Rahim : Sohel : Tarek = (12000 × 9) : (9000 × 4) : (15000 × 9)
= 108000 : 36000 : 135000
= 12 : 4 : 15


∴ Tarek's share = {6975 × (15/31)}
= 3375 Taka

Question: If 2 kg of metal, of which 1/3 is zinc and the rest is copper be mixed with 3 kg of metal of which 1/4 is zinc and the rest is copper, What is the ratio of zinc to copper in the mixture?

Solution:
Zinc = {2 × (1/3)} + {3 × (1/4)} = 17/12
Copper = 5 - (17/12) = 43/12

∴  Zinc : Copper = (17/12) : (43/12)
= 17 : 43

Question: A man invested Tk. 18000 in Tk. 100 shares of a company at 25% premium. If the company declares 6% dividend at the end of the year, then how much does he get?

Solution:
Number of shares = 18000/125
= 144
Face value = Tk. (100 × 144)
= Tk. 14400
∴ Annual income = Tk. (6/100) × 14400
= Tk. 864

Question: Sahil and Nitish rent a stable for 9 months. Sahil puts in 84 horses for 5 months. How many horses can Nitish put in remaining month, if Nitish pay twice of Sahil?

Solution:
Let X be the number of horses put by the Nitish for 4 months;
ATQ,
(84 × 5)/(X × 4)= 1/2
⇒ 420/4x = 1/2
⇒ 4x = 840
∴ x = 210