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.

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Satt Academy · Accepted Answer

we know, I=prt100, where I=Interest; p=Principal; T=time Here, according to question for 1st & 2nd part 4000×x×1100+5000×y×1100=320.......(i) and, 5000×x×1100+4000×x×1100=310.......(ii) Now, from (i) we have, 4000x100+5000y100=320 ⇒4000x+5000y100=320 ⇒4000x+5000y=320×100 ⇒4x+5y=32........(iii) again, from (ii) we have, 5000x100+4000y100=310 ⇒5000x+4000y100=310 ⇒5000x+4000y=310×100 ⇒1000(5x+4y)=31×1000 ⇒5x+4y=31.......(iv) Now, we have (iii)×4⇒16x+20y=128 (iv)×5⇒25x+20y=155 ⇒-9x=-27 x=-27-9 Now, putting x=3 in (iii) 4×3+5y=32 ⇒12+5y=32 ⇒5y=32-12 ⇒5y=20 ⇒y=204=4The required value, x= 3 & y = 4 .

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