A depositor deposited Tk. 4,000 at x% simple interest and Tk. 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 Tk. 4,000 at y% simple interest, he would receive annual interest of Tk. 310. Find the value of x and y.
(Interest)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

প্রশ্নটিতে বলা হয়েছে, 4,000 টাকা x% এবং 5,000 টাকা y% সুদে ডিপোজিট করলে বছর শেষে মোট 320 টাকা সুদ পাওয়া যায়। এরপর বলা হয়েছে, 5,000 টাকা x% এবং 4,000 টাকা y% সুদে ডিপোজিট করলে বছর শেষে মোট 310 টাকা সুদ পাওয়া যায়। আপনাকে x এবং y এর মান বের করতে হবে।

We know, $I = \frac{p r t}{100}$

Where, I = Interest; p = Principal; t = Time

Here, according to question for 1^st & 2^nd part $\frac{4000 \times x \times 1}{100} + \frac{5000 \times y \times 1}{100} = 320 . . . . . . . . (i)$

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

Now, from (i) we have,

$\frac{4000 x}{100} + \frac{5000 y}{100} = 320 \Rightarrow \frac{4000 x + 5000 y}{100} = 320 \Rightarrow 4000 x + 5000 y = 320 \times 100 \Rightarrow 1000 (4 x + 5 y) = 32 \times 1000 \Rightarrow 4 x + 5 y = 32 [D i v i d e b o t h s i d e b y 1, 000] ∴ 4 x + 5 y = 32 . . . . . . . . (i i i)$

Again, from (ii) we have,

$\frac{5000 x}{100} + \frac{4000 y}{100} = 310 \Rightarrow \frac{5000 x + 4000 y}{100} = 310 \Rightarrow 5000 x + 4000 y = 310 \times 100 \Rightarrow 1000 (5 x + 4 y) = 31 \times 1, 000 \Rightarrow 5 x + 4 y = 31 [D i v i d e b o t h s i d e b y 1, 000] ∴ 5 x + 4 y = 31 . . . . . . . (i v)$

$N o w, (i i i) \times 4 - (i v) \times 5, w e h a v e$

$\frac{16 x + 20 y = 128 25 x + 20 y = 155}{- 9 x = - 27} \Rightarrow x = \frac{- 27}{- 9} ∴ x = 3$

$N o w, p u t t i n g x = 3 i n (i i i) (4 \times 3) + 5 y = 32 \Rightarrow 12 + 5 y = 32 \Rightarrow 5 y = 32 - 12 \Rightarrow 5 y = 20 ∴ y = \frac{20}{5} = 4$