Bangladesh Bank Assistant Director written examination math solutions are given below for the year 2010 and 2011 –

**Bangladesh Bank AD written exam math solution 2011 –**

**01.** Two cars race around a circular track in opposite directions at constant rates. They start at the same point and meet every 30 seconds. If they move in the same direction, they meet every 120 seconds. If the track is 1800 meter long, what is the speed of each car?

**Solution:**

Let “x” be the speed of the faster car and “y” be the speed of the slower car

In case of same direction,

(x + y) * 30 = 1800

Or, 30x + 30y = 1800 ………… (1)

In case of opposite direction,

(x – y) * 120 = 1800

Or, 120x – 120y = 1800 ………. (2)

(1)*4 + (2) >>>

240x = 9000

Or, x = 37.5 m/s = 37.5*18/5 km/hr = 135 km/hr

(1)*4 – (2) >>>

– 240y = – 5400

Or, y = 22.5 m/s = 22.5*18/5 km/hr = 81 km/hr Ans.

**02.** A printer quotes a price of taka 7,500 for printing 1,000 copies of a book and Taka 15,000 for printing 2,500 copies. Assuming a linear relationship and 2,000 books are printed, find (a) the variable cost per book, (b) the average cost per book and (c) the fixed cost.

**Solution:**

(a) 1000 copies need 7500 Tk

2500 copies need 15000Tk

Extra 1500 copies need = 15000 – 7500 = 7500Tk

So, cost for first 1000 copies is fixed and next all are variable

We can get variable cost per book = 7500/1500 = 5 Tk Ans.

(b) As cost function is linear and total cost for printing first 1000 copies is 7500 Tk and the variable cost for per book is 5 Tk.

So, more 1000 copies cost = 5*1000 = 5000 Tk

To print 2000 books we need = (7500 + 5000) = 12,500 Tk

Average cost = 12500/2000 = 6.25 Tk Ans.

(c) Fixed cost = (7500 – 5000) = 2500 Tk Ans.

**03.** The length of a rectangle is twice its width. If the length is increased by 4 inches and the width is decreased by 3 inches, a new rectangle is formed whose perimeter is 62 inches. What is the length of the original rectangle?

**Solution:**

Let, width = x

Length = 2x

According to question,

2{(x + 4) + (2x – 3)} = 62

Or, 2x + 8 + 4x – 6 = 62

Or, 6x = 62 – 2

Or, 6x = 60

Or, x = 10

So, length = 2*10 = 20 inch. Ans.

**Bangladesh Bank AD Written exam math answer 2010 – **

**01.** Tanim bought some oranges. He gave 1/2 of them to his sister,1/4 of the remainder to his neighbor, 3/5 of those left to his children and had 6 left in the end. How many oranges did Tanim buy?

**Solution:**

Let, total oranges = x

Sister got = x/2

Neighbor got = 1/4 of x/2 = x/8

Left = x/2 – x/8 = 3x/8

Children got = 3/5 of 3x/8 = 9x/40

Left = 3x/8 – 9x/40 = 6x/40

According to question,

6x/40 = 6

Or, x/40 = 1

Or, x = 40 Ans.

**02.** The length of rectangular plot is greater than its breadth by 20 meters. If the perimeter of the plot is 160 meters, what is the area of the plot in square meters?

**Solution:**

Let, breadth be x meters and length be (x + 20) meters

According to the question,

2x + 2(x + 20) = 160

Or, 4x + 40 = 160

Or, 4x = 160 – 40

Or, x = 120/4 = 30

So, breadth = 30 meters and length =30 + 20 = 50 meters.

Area of the pot = (50 × 30) = 1500 sq. meters. Ans.

**03.** Three partners A, B & C start a business. Twice the investment of A is equal to thrice the capital of B is 4 times the capital of C. They share the profit in the ratio of their capital. In a particular year, the gross profit is Tk. 250000 and the administrative expenses are 20 % of the gross profit. Find the share of profit each partner.

**Solution:**

Let us consider, capital of C = x

So, capital of B = 4x

According to question,

2A = 3B or, A = 3B/2 = 12x/2 = 6x

Ratio of capital as well as profit of the three partners = 6x : 4x : x = 6 : 4 : 1

Administrative expenses = 20% of 2,50,000 = 20,000

So, net profit = 2,50,000 – 50,000 = 2,00,000

Share of A = (2,00,000*6)/11 = 1,09,090.90 Tk.

Share of B = (2,00,000*4)/11 = 72,727.27 Tk.

Share of C = (2,00,000* 1)/11 = 18,181.81 Tk Ans.