Bangladesh Bank Math solution for written examination of Assistant Director position for the 2012 & 2013. BB AD Written exam math solution for the 2012 and 2013 circular.

**Bangladesh Bank AD Math solution 2012 –**

**01.** A series has 3 numbers a, ar, ar^2. In the series, the first term is twice of the second term. What is the ratio of the sum of the first 2 terms to the sum of the last 2 terms?

**Solution:**

Let, the third term, ar^2 = x

So, according to question, second term, ar = 2X and first term, a = 4x

So, (a + ar) : (ar + ar^2)

Or, (4x + 2x) : (2x + x)

Or, 6x : 3x

Or, 2 : 1 Ans.

**02.** Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2. A new alloy X is formed by mixing the two alloys A & B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X?

**Solution:**

Let F = the first basic element and S = the second basic element.

Alloy A: Since F:S = 5:3, so amount of F = 5/8 & amount of S = 3/8

Alloy B: Since F:S = 1:2, so amount of F = 1/3 & amount of S = 2/3

Now, ratio of alloy A & B in new alloy X is 4:3

amount of F in the new alloy X = (5/8)*4 + (1/3)*3 = 7/2

amount of S in the new alloy X = (3/8)*4 + (2/3)*3= 7/2

so ratio of F & S in new alloy X = (7/2)/(7/2) = 1/1 = 1:1 Ans.

**Bangladesh Bank AD Written Math Solution 2013**

**01.** A, B and C do a job alone in 20, 30 and 60 days respectively. In how many days can A do the job if he is assisted by B & C?

**Solution:**

(A+B+C) work 1 days = 1/20 + 1/30 + 1/60 = 1/10

With help of B & C, A can do 1/10 part work in 1 day

,, ,, ,, ,, ,, ,, 1 (whole) part in 10 days Ans.

**02.** A bus is traveling with 52 passengers. When it arrives at a stop, Y passengers get off and 4 get inside at the next stop one-third of the passengers get off and 3 get on. There are 25 passengers. Find out how many passengers got off at the first stop?

**Solution:**

52 passengers

Y passengers get off making it 52 – y

4 get on making it 52 – y + 4

At the next stop one-third of the passengers get off and 3 get on to make it 25

(52 – y + 4) – 1/3(52 – y + 4) + 3 = 25

=> {2(52 – y + 4) + 9}/3 = 25

=> 104 – 2y +8 + 9 = 75

=> – 2y = – 46

=> y = 46/2

So, y=23

Hence, 23 passengers got off at the first stop. Ans.

**03.** An Eskimo leaves its igloo and travels 3 km north, then 8 km east and finally 3 km north to reach the north pole. How many km does he have to travel to return to his igloo in a straight line?

Suppose, the Eskimo started from the point O, traveled 3km north to

R, then from R, traveled 8km east to S, and finally from S traveled

3km north to A.

By joining A with O with a direct line (the blue line) and rearranging

OR to PS and RS to OP, we get the right angle triangle AOP of which

AP = 3+3 = 6, OP = 8.

Therefore, AO = √(AP² + OP²) = √(8²+ 6²) = 10