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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: a
Explanation:
$$\eqalign{ & {\text{Let}}\,{1^{st}}\,{\text{part}}\,{\text{is}}\,x\,{\text{and}}\,{2^{nd}}\,{\text{part}}\,{\text{is}}\,\left( {6000 – x} \right) \cr & {\text{According}}\,{\text{to}}\,{\text{question}}, \cr & {\frac{{x \times 2 \times 6}}{{100}}} = \frac{{ {\left( {6000 – x} \right) \times 3 \times 8} }}{{100}} \cr & 12x = 144000 – 24x \cr & \,36x = 144000 \cr & \,x = \frac{{144000}}{{36}} = Rs.\,4000 \cr & {1^{st}}\,{\text{part}} = Rs.\,4000 \cr & {2^{nd}}\,{\text{part}} = Rs.\,2000 \cr} $$

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