Bangladesh Development Bank recruitment Exam

Written Exam
8. Solve the following mathematical problems:
a. The profit of a company is given in Taka by P = 3{x^2} - 35x + 50, where x is the amount in Taka spent on advertising. For what values of x does the company make a profit?
Solution:
Given that,
P = 3{x^2} - 35x + 50 > 0
\Rightarrow 3{x^2} - 30x - 5x + 50 > 0
\Rightarrow 3x(x - 10) - 5(x - 10) > 0
\Rightarrow (x - 10)(3x - 5) > 0

b.  An amount of Tk. 7200 is spent to cover the floor of a room by carpet. An amount of Tk. 576 would be saved if the breadth were 3 metres less. What is the breadth of the room?
Solution:
c. Find the three-digit prime number whose sum of the digits is 11 and each digit representing a prime number. Justify your answer.
Solution:
d. If \frac{a}{{q - r}} = \frac{b}{{r - p}} = \frac{c}{{p - q}} then show that a+b+c=pa+qb+rc
Solution:
Let, \frac{a}{{q - r}} = \frac{b}{{r - p}} = \frac{c}{{p - q}}=k
\therefore \frac{a}{{q - r}} =k
\Rightarrow a=k(q-r)
or, \frac{b}{{r - p}} = k
\Rightarrow b=k(r-p)
or,\frac{c}{{p - q}}=k
\Rightarrow c=k(p-q)
বামপক্ষ,
a + b + c
= k(q - r) + k(r - p) + k(p - q)
= k(q - r + r - p + p - q)
= k \times 0
= 0
ডানপক্ষ,
pa + qb + rc
= pk(q - r) + qk(r - p) + rk(p - q)
= pkq - pkr + qkr - qkp + rkp - rkq
= 0
\therefore বামপক্ষ=ডানপক্ষ

e. Prove that a cyclic parallelogram must be a rectangle.
Solution:

f. After traveling 108km, a cyclist observed that he would have required 3 hrs, less if he could have travelled at a speed 3km/hr more. At what speed did he travel?
Solution:

g. Solve: \frac{x}{2} + \frac{6}{y} = 9…………(i); \frac{x}{3} + \frac{2}{y} = 4………. (ii)
Solution: