BKB written examination written math solution 2017 for the post of Officer. Bangladesh Krishi Bank Officer position written exam math solution 2017.

1. Proof of identity of 115 people was verified. 65 of them had Passport, 30 of them had both Passport and Voter ID. However, 15 of them could not produce any identity documents. How many of them showed up only with Voter ID?

**Solution:**

We know:

n(Total) = n(total passport) + n(total voter ID) – n(both passport and voter ID) + n(none)

According to the question:

115 = 65 + n(total voter ID) – 30 + 15

n(total voter ID) = 65.

So, only Voter ID = (total voter ID) – (both passport and voter ID) = 65 – 30 = 35.

Answer: 35.

2. Rafiq, Shafiq, and Arif can alone complete a project in 10 days, 20 days, and 10 days respectively. Rafiq started working on the project alone. Shafiq joined the project after 2 days. After working together for 4 days both Rafiq and Shafiq left the project and Arif got in. How many days it took to complete the entire project?

**Solution:**

Rafiq can do in 1 day = 1/10 of the work

Shafiq can do in 1 day = 1/20 of the work

Arif can do in 1 day = 1/10 of the work

Rafiq and Shafiq completed in first 6 days = 6/10 + 4/20 = 16/20 = 4/5 of the work.

So, Arif did the remaining (1 – 4/5) = 1/5 of the work in = (1/5)/(1/10) = 2 days.

So, it took 6+2 = 8 days to complete the entire project.

Answer: 8 days.

3. Mr. Rashid has saved Taka 1200 from his first month’s salary. He plans to increase his monthly savings by Taka 100 in every following month. How much time would it take to save Taka 106200?

**Solution**

Suppose, it will take ‘n’ months to save Taka 106200.

Here, the savigns in the first month, a = Taka 1200.

Increase in savings in each month, d = Taka 100.

According to the question:

(n/2){2×1200 + 100(n-1)} = 106200

n(1200 + 50n – 50) = 106200

n² + 23n = 2124

n² + 59n – 36n – 2124 = 0

(n+59)(n-36) = 0

n = 36 (as n = -59 is not accepted on the ground that the number of terms cannot be a negative number).

Ans: 36 months or 3 years.

4. Solve the equation : 2{(x+3)/(x-3)}² – 7{(x+3)/(x-3)} + 6 = 0

**Solution:**

Suppose, (x+3)/(x-3) = a

So, 2{(x+3)/(x-3)}² – 7{(x+3)/(x-3)} + 6 = 0

=> 2a² – 7a + 6 = 0

=> 2a² – 4a – 3a + 6 = 0

=> 2a(a-2) – 3(a-2) = 0

=> (a-2)(2a-3) = 0

=> a = 2 or 3/2

So, either

(x+3)/(x-3) = 2

2x – 6 = x + 3

x = 9.

or,

(x+3)/(x-3) = 3/2

3x – 9 = 2x + 6

x = 15

Ans: 9 or 15.

5. The area of a rectangle is 1200 square meter. If the length of the rectangle is reduced by 10 meters, it becomes a square. Calculate the length of the diagonal of the rectangle.

**Solution:**

Given,

If the length of the rectangle is reduced by 10 meters, it becomes a square.

That implies: the length of the rectangle is 10 meters more than its width.

Suppose, the width of the rectangle is = x meters.

According to the question:

x(x+10) = 1200

x² + 10x – 1200 = 0

(x+40)(x-30) = 0

x = 30, (as x = -40 is not acceptable on the ground that the value of a length cannot be a negative number)

So, the width of the rectangle is = 30 meters, and

the length of the rectangle is = 30+10 = 40 meters.

So, the length of the diagonal of the rectangle is = √(40²+30²) = 50 meters.

Answer: 50 meters.

6. A Rhombus has an area of 120 square meters and the length of its one diagonal is 10 meters. Calculate the perimeter of the Rhombus.

**Solution:**

Suppose, the length of a side of the rhombus is = a meters, and that of the other diagonal is = d meters.

We know, area of a rhombus = (product of the lengths of the diagonals)/2

=> 120 = (10×d)/2

=> d = 24 meters.

Again, We know:

4a² = 24² + 10²

a² = 169

a = 13

So, the perimeter of the rhombus is = 4a = 4×13 = 52 meters.

Answer: 52 meters.

7. The area of an equilateral triangle is 3√3 square meter. Determine the area of a circe inscribed within the triangle.

**Solution:**

Suppose, the length of a side of the triangle is = a meters.

According to the question:

(√3/4)a² = 3√3

=> a² = 12

=> a = √12 = 2√3 meters.

We know, if a circle is inscribed to an equilateral triangle, the length of is radius is (1/2√3) times the length of a side of the triangle.

So, the radius of the circle is= 1/2√3 × 2√3 = 1 meter.

So, the area of the circle is = π×1² = π ≈ 3.1416 square meters.

Answer: 3.1416 square meters.