Problem: A depositor deposited Tk. 4,000 at x% simple interest and Tie 5,000 at y% simple interest. He received annual interest of Tk. 320 on his deposited amounts at the year end. if he could deposit Tk. 5,000 at x% simple interest and Th. 4,000 at y% simple interest. hewould receive annual interest of Tk. 310. Find the value of x and y.

Correct Answer: The required value, x = 3 & y = 4.

Explanation:

We know, I = $\frac{Prt}{100}$,

WhereI = Interest

p = Prinicipal

t = Time

According to the question for 1$^{st}$ & 2$^{st}$ part

$\frac{4000\times x\times 1}{100}+\frac{5000\times y\times 1}{100}$ = 320………………(i)

And,$\frac{5000\times x\times 1}{100}+\frac{4000\times y\times 1}{100}$= 310 ………….(ii)

Now, from (i) we have,$\frac{4000x}{100}+\frac{5000y}{100}$ = 320

=> $\frac{4000x+5000y}{100}$ = 320

=> 4,000x + 5,000y = 320 x 100

=> 1,000(4x + 5y) = 32 X 1,000

=> 4x + 5y = 32

4x + 5y = 32………… (iii)Again, from (ii) we have,

$\frac{4000x}{100}+{5000y}{100}$=310

=> $\frac{4000x+5000y}{100}$ = 310

=> 5,000x+ 4,000y = 310 x 100

=> 1,000(5x+ 4y) = 31 x 1,000

=> 5x + 4y= 315x + 4y= 31…………… (iv)

Now, we have

(iii) $\times$ =>16x+ 20y= 128

(iv) $\times$ =>25x+20y = 155

-9x = -27 [ বিয়োগ করা হল]

=> x = $\frac{-27}{-9}$

x=3Now, putting x = 3 in (iii)(4 x 3)+ 5y= 32

=> 12+5y=32

=> 5y=32- 12

=> 5y=20

=> y = $\frac{20}{5}$

y=4