Assistant Director written examination math solution of Bangladesh Bank. Bangladesh Bank AD written examination math solutions 2015 are given below –

**01.** A bus hired at the cost of Tk. 2400 and it was decided that every student would share the cost equally. But 10 more students joined as a result the fare decreased by Tk. 8 per person. How many students were travelling in the bus?

**Solution:**

Let, total students = x, so average fair = 2400/x

Later, 10 more students have come, so average fair = 2400/(x + 10)

According to question,

2400/x – 2400/(x + 10) = 8

Or, {2400(x + 10) – 2400x}/x(x + 10) = 8

Or, (2400x + 24000 – 2400x)/x(x + 10) = 8

Or, 24000/x(x + 10) = 8

Or, 2400 = 8×2 + 80x

Or, 8×2 + 80x – 24000 = 0

Or, x2 + 10x – 3000 = 0

Or, x2 + 60x – 50x – 3000 = 0

Or, (x + 60)(x – 50) = 0

Or, x = 50 Ans.

**02.** The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and of the girls is 15.4 years. Find the ratio of number of boys to girls in the class.

**Solution:**

Let us consider, number of boys = x and girls = y

According to question,

15.8(x + y) = 16.4x + 15.4y

Or, 15.8x + 15.8y = 16.4x + 15.4y

Or, 16.4x – 15.8x = 15.8y – 15.4y

Or, 0.6x = 0.4y

Or, x/y = 0.4/0.6 = 4/6 = 2/3 Ans.

**03.** If (x + 1/x) = 3 then the value of (x2 + 1/x2) = ?

**Solution:**

(x + 1/x) = 3

Or, (x + 1/x)2 = 3^2

Or, x2 + 2.x.1/x + 1/x2 = 9

Or, x2 + 1/x2 = 9 – 2 = 7 Ans.

**04.** The percentage profit earned by selling an article for Tk. 1920 is equal to the percentage loss incurred by selling the same article for Tk. 1280. At what price should the article be sold to make 25% profit?

**Solution:**

Here, both the article is same as well as cost price and percentage of profit and loss.

Let cost price of the article = x Tk.

In case of first condition,

Percentage of profit = {(1920 – x)100}/x

In case of second condition,

Percentage of loss = {(x – 1280)100}/x

According to question,

{(1920 – x)100}/x = {(x – 1280)100}/x

Or, 1920 – x = x – 1280

Or, x + x = 1920 + 1280

Or, 2x = 3200

Or, x = 1600

So, cost price = 1600 Tk.

At 25% profit, sell price will be = 1600 + 1600*25/100

= 1600 + 400

= 2000 Tk. Ans.

**05.** A can do a piece of work in 10 days while B can do it in 15 days. They work together for 5 days and the rest of the work is done by C in 2 days. If they get Tk. 4500 for the whole work, how should they divide the money?

**Solution:**

Here, in 1 day A can do 1/10 part

So, in 5 days A do = 5/10 = 1/2 part

Again, in 5 days B do = 5/15 = 1/3 part

Rest of the work done by C = 1 – (1/2 + 1/3) = 1 – 5/6 = 1/6

So, A’s share = 4500/2 = 2250 Tk.

B’s share = 4500/3 = 1500 Tk.

C’s share = 4500/6 = 750 Tk. Ans.

**06.** ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the area of the square?

Here, ABO is a right triangle

So, AB2 = BO2 + AO2 = 9 + 9 = 18

Or, Ab = √18 = 3√2

So, area of the square ABCD = (3√2)2

= 18 sq. unit Ans.

Bangladesh Bank Assistant Director written exam math solution 2015. BB AD Written Math Questions and solutions.