Question

divide 24000 in two parts such that the simple interest of the first part for 4 years at 12% per annum is equal to the simple interest on second part for 6 years at 16% per annum​

Answer 1

Answer:

Given,

Total amount = 24,000

Let first part = x ⇒ Second part = 24000 - x

∵ Annual rate of simple interest in first part = 12%,

Time = 4 years,

Also, simple interest formula,

I=\frac{P\times r\times t}{100}I=

100

P×r×t

Where,

P = principal, r = rate per period, t = number of periods,

So, the simple interest in first part,

I_1=\frac{x\times 12\times 4}{100}I

1

=

100

x×12×4

=\frac{48x}{100}=

100

48x

Similarly,

Annual rate of simple interest in second part = 16%,

Time = 6 years,

So, the simple interest in second part,

I_2=\frac{96(24000-x)}{100}I

2

=

100

96(24000−x)

According to the question,

I_1=I_2I

1

=I

2

\implies \frac{48x}{100}=\frac{96(24000-x)}{100}⟹

100

48x

=

100

96(24000−x)

48x = 96(24000 - x)48x=96(24000−x)

48x = 2304000 - 96x48x=2304000−96x

48x + 96x = 230400048x+96x=2304000

144x = 2304000144x=2304000

x = 16000x=16000

Hence, the parts are 16000 and 8000

Step-by-step explanation:

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