Pubali Bank Ltd. || Junior Officer (2019) || 2019

Let the initial investment of A and B is 18x and 7x
After 4 months from the start of business,
A invest Rs. 2000 more for each eight months.
Then total investment of A
 

=18x×4+(18x+2000)×8=72x+144x+16000=216x+16000

After 4 months, from the start of business,
B invest Rs. 7000 more for each eight months.
Total investment by B
 

=7x×4+(7x+7000)×8=28x+56x+56000=84x+56000

According to the question,
 

⇒216x+1600084x+56000=21

⇒ 216x + 16000 = 168x + 112000
⇒ 216x - 168x = 112000 - 16000
⇒ 48x = 96000
⇒ x = 2000
Total initial investment of A and B
= (18 + 7) × 2000
= Rs. 50000

প্রশ্নে বলা হচ্ছে, 4 বছর পূর্বে A এর বয়সের অর্ধেক এবং B এর বয়সের এ গুণের অনুপাত 5 : 12 ছিল। 8 বছর পর A এর বয়সের অর্ধেক B এর বয়সের চেয়ে 2 বছর কম হবে। B এর বর্তমান বয়স কত?

Suppose, age of 'A' age and 'B' 4 years ago be x and y respectively

According to the first condition,

$\frac{x}{2} : 4y = 5 : 2$

$\Rightarrow \frac{x}{2} \times 12 = 4y \times 5$

$\Rightarrow \Rightarrow 6x = 20 y$

$\therefore x = \frac{10 y}{3} . . . . .. . . . . .. . .\left(i\right)$

∴ After 8 years hence, age of A = x+4+8= (x+12)

And after 8 years hence, age of B = y +4 +8=(y+12)

$\frac{1}{2} \left(x + 12\right) = \left(y + 12\right) - 2$

$\Rightarrow \frac{x+12}{2} = y + 10$ 

$\Rightarrow x+ 12 = 2y + 20$

$\Rightarrow x - 2y = 20 - 12$

$\Rightarrow \frac{10y}{3} - 2y [ Since x = \frac{10y}{3}]$

$\Rightarrow 4y = 24$

$\therefore y = \frac{24}{4} = 6$

Hence, the present age of B = 6 + 4 = 10 years.