Question

divide 6000 into two parts such that the simple interest on the first part for 9 months at 12%per annum is equal to the simple interest on the second part for 3/2 years at 10% per annum​

Answer 1

≡QUESTION≡

Divide 6000 into two parts such that the simple interest on the first part for 9 months at 12%per annum is equal to the simple interest on the second part for 3/2 years at 10% per annum​.

                                                                                   

║⊕ANSWER⊕║

Let, First part be Rs x

Then second part = Rs(6000 - x)

S.I = P*R*T

=> x * 12/100 * 3/4  =  (6000 - x) * 3/2 * 10/100

=> 9/100 * x = (6000 - x) * 3/2 * 10/100

=> 9x = 90000 - 15x

=> 24x = 90000

=> x = 3750

∴ First part = Rs 3750

second part = Rs (6000 - 3750)

                     = Rs 2250

                                                                                           

Answer 2

AnswEr :

$\textsf{Let one Part be Rs. n and another be Rs. (6000 - n)}$

$\bf{First\:Part}\begin{cases}\sf{Principal = Rs. \:n}\\\sf{Time = 9 \:months = \cancel\dfrac{9}{12} = \dfrac{3}{4} \:yr}\\ \sf{Rate = 12\% \:p.a.}\end{cases}$

$\bf{Second\:Part}\begin{cases}\sf{Principal = Rs. \:(6000 - n)}\\\sf{Time = \dfrac{3}{2} yr}\\ \sf{Rate = 10\% \:p.a.}\end{cases}$

$\rule{100}{2}$

$\bigstar \:\boxed{\sf Simple \:Interest=\dfrac{Principal \times Rate \times Time}{100}}$

$\rule{250}{1}$

• According to the Question Now :

$:\implies\textsf{SI on First Part = SI on Second Part}\\\\\\:\implies\sf\dfrac{(PRT)_1}{\cancel{100}}=\dfrac{(PRT)_2}{\cancel{100}}\\\\\\:\implies\sf(PRT_1)=(PRT_2)\\\\\\:\implies\sf\bigg(n \times \cancel{12} \times \dfrac{3}{\cancel4}\bigg) = \bigg((6000-n) \times \cancel{10} \times \dfrac{3}{\cancel2}\bigg)\\\\\\:\implies\sf(n \times 3 \times 3) = (6000 - n) \times 5 \times 3\\\\\\:\implies\sf 9n = 90000 - 15n\\\\\\:\implies\sf15n + 9n = 90000\\\\\\:\implies\sf24n = 90000\\\\\\:\implies\sf n = \cancel\dfrac{90000}{24}\\\\\\:\implies\sf n = Rs.\:3750$

$\rule{250}{2}$

$\bullet\:\textsf{First Part = n = \textbf{Rs. 3750}}\\\\\bullet\:\textsf{Second Part = (6000 - n) = \textbf{Rs. 2250}}$