ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: The ratio of the present ages of Riya and her mother is 3 : 7. The mother’s age at the time of Riya’s birth was 20 years. Find the mother’s present age.

Solution:
Present ratio is 7 : 3.
Let actual ages are 7x and 3x.

∴ 7x - 3x = 20
⇒ 4x = 20
∴ x = 5

Hence the mother’s present age 7 × 5 = 35 years

Question: Joyanta started a business and he invested in 38000, After some month, Omar came to join with him and invest 28500. The end of the year the total profit was divided among them into ratio form 16 : 8. Find after how many months did Omar join.

Solution:
we can assume that Omar join into business after x months.
So Omar money was invested for (12 - x) months.

(38000 × 12)/{28500 × (12 - x)} = 2/1 (The given ratio of 16 : 8 is equivalent to 2 :1)
⇒ 456000 = 28500(12 - x) 
⇒ 456000 = 57000(12 - x)
⇒ 57(12 - x) = 456
⇒ 12 - x = 8
∴ x = 4

After 4 months Omar join the business.

Question: What yearly income can be earned by investing Tk. 14400 in 15% stock at Tk. 120?

Solution:
From Tk. 120 earn 15
From Tk. 1 earn 15/120
From Tk. 14400 earn (15 × 14400)/120 
= 1800

Question: 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally?

Solution:
Let the quantity of the wine in the cask originally be x litres
Then,
quantity of wine left in cask after 4 operations = [x(1 - 8/x)⁴] litres
[x(1 - 8/x)⁴]/x = 16/81
⇒ [1 - 8/x]⁴ = (2/3)⁴
⇒ 1 - 8/x = 2/3
⇒ 8/x = 1/3
∴ x = 24

Question: The perimeter of a rectangle is 64 cm. If the ratio of the lengths of two adjacent sides is 7 : 9, find the lengths of these sides.

Solution:
Perimeter of a rectangle = 2(Length + Breadth)
Also Length :  Breadth = 9 : 7
Let actual values are 9x and 7x.

Hence,
2(9x + 7x) = 64
⇒ 16x = 32
∴ x = 2

∴ sides will be of 14 cm and 18 cm.

Question: A 9% stock yields 8%. The market value of the stock is-

Solution:
Earn Tk. 8 when market value Tk. 100
Earn Tk. 1 when market value Tk. 100/8
Earn Tk. 9 when market value Tk. (100 × 9)/8
= Tk. 112.5

Question: Sayed started a software business by investing Tk. 20000. After six months, Rafi joined him with a capital of Tk. 30000. After 3 years, they earned a profit of Tk. 13950. What was Sayed’s share in the profit?

Solution:
Ratio of capitals of Sayed and Rafi
= (20000 × 36) : (30000 × 30)
= 720000 : 900000
= 4 : 5.

Sayed’s share is = Tk. (13950 × 4)/9 = Tk. 6200.

Question: A merchant has 1000 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:
Profit of first part                                Profit of second part

So, ratio of 1st and 2nd parts = 4 : 6 = 2 : 3. 
Therefore, Quantity of 2nd kind = (3/5) × 1000 kg = 600 kg.

Question: There are 145 students in the first three standards. The ratio of number of students in the first and the second standards is 2 : 3, while that of students in standards second and third is 4 : 3. Find the number of students in 2nd standard.

Solution:
Total students = 145.
Ratio of students in 1st and 2nd standards = 2 : 3 = (2 × 4) : (3 × 4) = 8 : 12

Ratio of students in 2nd and 3rd standards = 4 : 3 = (4 × 3) : (3 × 3) = 12 : 9
Hence combined ratio i.e. 1st : 2nd: 3rd is = 8 : 12 : 9.

∴ Number of students in 2nd standard = (145 × 12)/29 = 60

Question: To produce an annual income of Tk. 1200 from a 12% stock at 90, the amount of stock required is-

Solution:
12% stock at 90 mean,
Stock face value 100 and market value 90

12 Taka can be produced from Tk. 100
1 Taka can be produced from Tk. 100/12
1200 Taka can be produced from Tk. (100 × 1200)/12 = Tk. 10000

Question: A, B and C started a business by investing Tk. 250000, Tk. 300000 and Tk. 350000 respectively. Find the share of B, out of an annual profit of Tk. 187200.

Solution:
Ratio of shares of A, B and C = Ratio of their investment
A : B : C = 250000 : 300000 : 350000
= 5 : 6 : 7

Share of B = Tk. [(187200 × 6)/ 18] = 62400.

Question: How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per Kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per Kg?

Solution:
By the rule of alligation:
C.P. of 1 kg sugar of 1st kind                               C.P. of 1 kg sugar of 2nd kind 

Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. 
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. 
Then,
7 : 3 = x : 27
or x = (7 × 27)/3 = 63 kg.

Question: Which number when added to each of the numbers 24, 32 and 42 would make the sums to be in continued proportion?

Solution:
Let the number to be added is x.

∴(24 + x)/(32 + x) = (32 + x)/(42 + x).
⇒ (24 + x)(42 + x) = (32 + x)²
⇒ 1008 + 66x + x² = 1024 + 64x + x²
⇒ 2x = 16
∴ x = 8.

Question: The capital stock of a company is Tk. 500000 and is divided into 5000 shares of common stock. If the company pays a dividend of Tk. 64000, what amount will Rakib receive for his 50 shares?

Solution:
5000 shares income Tk. 64000
1 share incomes Tk. 64000/5000
50 shares income Tk. (64000 × 50)/5000
= Tk. 640

Question: Abu and Salim started a partnership business investing some amount of money in the ratio of 4 : 6. Shakeel joined them after six months with an amount equal to that of Salim. In what proportion should the profit at the end of one year be distributed among Abu, Salim and Shakeel?

Solution:
As (4 : 6 is equivalent to 2 : 3)
So let the initial investment of money ratio of Abu and Salim is 2x and 3x.
So Abu , Salim and Shakeel ratio of investment will be ( Abu : Salim : Shakeel ) = (2x × 12) : (3x × 12) : (3x × 6) = 24 : 36 : 18 = 4 : 6 : 3

Question: The cost of Type 1 rice is Tk. 15 per kg and Type 2 rice is Tk. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is-

Solution:
Let the price of the mixed variety be Rs. x per kg.
By the rule of alligation, we have :
Cost of 1 kg of type 1 rice                                     Cost of 1 kg of type 2 rice 

∴(20 - x)/(x - 15) = 2/3 
⇒ 60 - 3x = 2x - 30
⇒ x = 18.

Question: If 6m - n = 4m + 13n, find the value of 2m + n : 2m - 3n.

Solution:
6m - n = 4m + 13n
⇒ 2m = 14n
∴ m = 7n.

∴ Required ratio = (2m + n : 2m - 3n)
= 14n + n : 14n - 3n
= 15n : 11n
= 15 : 11

Question: A corporation declares an annual dividend of 5%. Mugdho owns 500 shares (par value Tk. 80). How much dividend will he receive?

Solution:
Amount of total shares = 500 × 80 = Tk. 40000

From Tk. 100 Mugdho gets dividends Tk. 5
From Tk. 1 Mugdho gets dividends Tk. 5/100
From Tk. 40000 Mugdho gets dividends Tk. (5 × 40000)/100 
= Tk. 2000

Question: Munna received Tk. 3000 as his share out of the total profit of Tk. 4500 which he and Raju earned at the end of one year. If Munna invested Tk. 60000 for 6 months, whereas Raju invested his amount for the whole year, what was the amount invested by Raju?

Solution:
Suppose Raju invested Tk. x.
Then, Ratio of their investments will be:
Munna : Raju = 60000 × 6 : x × 12 = 360000 : 12x

ATQ,
360000/12x = 3000/1500
∴ x = 15000

Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

Solution:
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' liters of water are 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)
Solving, we get P = 10 liters

Question: The ratio of the measures ∠A and ∠B of a triangle ABC is 3 : 2. The ratio of the measures of ∠B and ∠C is 4 : 5. Find the measure of largest angle of the triangle ABC.

Solution:
∠ A : ∠ B = 3 : 2.
∠ B : ∠ C = 4 : 5.
∴ ∠ A : ∠ B : ∠ C = 6 : 4 : 5.
Let actual values are 6x, 4x and 5x.

So
6x + 4x + 5x = 180° 
⇒ 15x = 180°
∴ x = 12°

So largest angle is  6(12°) = 72°

Question: A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is-

Solution:
From Tk. 100 one can earn dividend Tk. 9
From Tk. 1 one can earn dividend Tk. 9/100
From Tk. 20 one can earn dividend Tk. (9 × 20)/100 = Tk. 9/5

If interest Tk. 12 then the market Value Tk. 100
If interst Tk. 1 then the market Value Tk. 100/12
If interst Tk. 9/5 then the market Value Tk. (100 × 9)/(12 × 5)
= Tk. 15

Question: The ratio of milk and water in a solution is 20 : 7 and after adding 5 liters of water in it the ratio of milk and water becomes 5 : 3, then find the final amount of water in the final solution.

Solution:
Let the initial amount of milk be 20x and of water 7x.
Ratio of milk and water after adding 5 litres,
20x/ (7x + 5) = 5/3
⇒ 60x = 35x + 25
⇒ 25x = 25
⇒ x = 1.

∴ Final amount of water in solution = 7x + 5 = 7 + 5 = 12 litres.

Question: A, B and C started a business each investing Tk. 10000. After 4 month A withdraws Tk. 3000, B withdraws Tk.4000, C invest Tk. 3000 more At the end of the years, a total profit was Tk. 32800. Find the share of C.

Solution:
Ratio of capital of A, B and C.
= (10000 × 4 + 7000 × 8) : (10000 × 4 + 6000 × 8) : (10000 × 4 + 13000 × 8)
= 96000 : 88000 : 144000
= 12 : 11: 18

Distributing the final profit of Tk. 32800 in the given ratio, the share of C becomes = (32800 × 18)/41 = 14400.

Question: A piece of string 70 cm in length was cut into pieces, the ratio of whose lengths was 3: 7. Find the length of longest piece.

Solution:
Total length = 70 cm.
Ratio is 3 : 7
∴ Length of longest piece is (70 × 7)/10 = 49 cm