Question

Divide Rs. 6000 into two parts so that simple interest on the first part for 2 years at 6% p.a. may be equal to the simple interest on the second part for 3 years at 8% p.a.
A.Rs. 4000, Rs. 2000
B.Rs. 5000, Rs. 1000
C.Rs. 3000, Rs. 3000
D.None of these

Answer 1

______✨ HEY MATE ✨______

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SOLUTION :-
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Let 1st part is x and 2nd part is (6000-x).

According to question,

(X*2*6/100) = ((6000-x)*3*8)/100;
12x = 144000- 24x;
Or, 36x = 144000;
Or, x = 144000/36 = Rs. 4000.
1st part = Rs. 4000;
2nd part = Rs. 2000.

So , Option (A) is the right answer ✔️

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Answer 2

Answer:

$\setlength{\unitlength}{.8mm}\begin{picture}(50,55)\thicklines\put(45,40){\vector(2,-1){20}}\put(35,40){\vector(-2,-1){20}}\put(23,44){\sf\large\underline{Rs. 6000 (Total)}}\put(2,25){ \star }\put(5,25){\sf{Principal = x}}\put(2,20){ \star }\put(5,20){\sf{Rate = 6\%}}\put(2,15){ \star }\put(5,15){\sf{Time = 2 year}}\put(45,25){ \star }\put(48,25){\sf{Principal = (6000 - x)}}\put(45,20){ \star }\put(48,20){\sf{Rate = 8\%}}\put(45,15){ \star }\put(48,15){\sf{Time = 3 year}}\put(0,50){\line(1,0){95}}\put(0,12){\line(1,0){95}}\put(0,12){\line(0,3){38}}\put(95,12){\line(0,3){38}}\end{picture}$

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

$\rule{160}{1}$

$\underline{\bf{\dag}\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\: Simple\:Interest_1=Simple\:Interest_2\\\\\\\dashrightarrow\tt\:\:\dfrac{(Principal \times Rate \times Time)_1}{100}=\dfrac{(Principal \times Rate \times Time)_2}{100}\\\\\\\dashrightarrow\tt\:\:(Principal \times Rate \times Time)_1 =(Principal \times Rate \times Time)_2\\\\\\\dashrightarrow\tt\:\:x \times 6 \times 2 =(6000 - x) \times 8 \times 3\\\\\\\dashrightarrow\tt\:\:12x = (6000 - x)24\\\\\\\dashrightarrow\tt\:\:x = (6000 - x)2\\\\\\\dashrightarrow\tt\:\:x = 12000 - 2x\\\\\\\dashrightarrow\tt\:\:x + 2x = 12000\\\\\\\dashrightarrow\tt\:\:3x = 12000\\\\\\\dashrightarrow\tt\:\:x = \dfrac{12000}{3} \\\\\\\dashrightarrow\tt\:\:\underline{\boxed{\tt x = 4000}}$

$\rule{100}{2}$

$\bullet\:\:\textsf{First Part = x = \textbf{Rs. 4000}}\\\bullet\:\:\textsf{Second Part = (6000 - x) = \textbf{Rs. 2000}}$