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35 votes
Aslam invested rs 210000part at 8% per annum and the rest at 6%per annum. if the annual incomes from both investment were the same, find the amount invested at each rate.

User Glaux
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1 Answer

16 votes
16 votes

a = amount invested at 8%

how much is 8% of "a"? (8/100) * "a", namely 0.08a.

b = amount invested at 6%

how much is 6% of "b"? (6/100) * "b", namely 0.06b.

we know the total amount invested is 210000, so whatever "a" and "b" might be, we know that a + b = 210000.

we also know that the yielded amount in interest is the same for both, so whatever 0.08a and 0.06b are, we know they're the same.


\begin{cases} a+b=210000\\\\ 0.08a=0.06b \end{cases}\hspace{5em}a+b=210000\implies b=210000-a \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.08a~~ = ~~0.06(210000-a)}\implies 0.08a=12600-0.06a\implies 0.14a=12600 \\\\\\ a=\cfrac{12600}{0.14}\implies \boxed{a=90000}\hspace{9em}\boxed{\stackrel{210000~~ - ~~90000}{b=120000}}

User SamMonk
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