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Consider the following statements<br>If a sum of money is lent at simple interest, then the<br>I - money gets doubled in 5 years if the rate of interest is $$16\frac{2}{3}$$ %<br>II - money gets doubled in 5 years if the rate of interest is 20%.<br>III - money becomes four times in 10 years if it gets doubled in 5 years.

Correct Answer: II alone is correct
$$\eqalign{ & {\text{Let sum be x}}{\text{.}} \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = x \cr & {\text{I - Time}} \cr & = \frac{{100 \times x}}{{x \times \frac{{50}}{3}}} \cr & = 6\,{\text{years(false)}} \cr & {\text{II}} - {\text{Time}} \cr & = \frac{{100 \times x}}{{x \times 20}} \cr & = 5\,{\text{years(True)}} \cr & {\text{III}} - {\text{Suppose sum}} = x. \cr & {\text{Then, S}}{\text{.I}}{\text{. }} = x \cr & {\text{Time }} = {\text{5 }}{\text{years}}{\text{.}} \cr & {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 20\% . \cr & {\text{Now, sum}} = x,\,{\text{S}}{\text{.I}}{\text{.}} = 3x\,{\text{and}}\,{\text{Rate}} = 20\% \cr & \therefore {\text{Time}} = \left( {\frac{{100 \times 3x}}{{x \times 20}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\,{\text{years}}(\text{false}) \cr & {\text{So, B alone is correct}}{\text{.}} \cr} $$

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$

Rahul borrowed a sum of Rs. 1150 from Amit at the simple interest rate of 6 p.c.p.a. for 3 Years. He then added some more money to the borrowed sum and lent it to Sachin for the same time at 9 p.c.p.a simple interest. If Rahul gains Rs. 274.95 by way of interest on borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Sachin ?

I had Rs. 10000 with me. Out of this money I lent some money to A for 2 years @ 15% simple interest. I lent the remaining money to B for an equal number of years @18% simple interest. After 2 years, I found that A had given me Rs. 360 more as interest as compared to B. The amount of money which I had lent to B must have been.

$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?

A person lent certain sum of money at 5% per annum simple interest and in 15 years the interest amounted to Rs 250 less than the sum lent. What was thesum lent (in Rs)?

A person lent certain sum of money at 10% per annum simple interest. In 20 years the interest amounted to Rs 500 more than thesum lent. What was the sum lent (in Rs)?

A sum of Rs.1550 was lent partly at 8% p.a. simple interest. The total interest received after 3 years was Rs.300. The ratio of the money lent at 5% to that lent at 8% is :

A sum of Rs. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Rs. 300. The ratio of the money lent at 5% to that lent at 8% is:

Some part of Rs 17500 was lent at the rate of 24% per annum simple interest and the remaining part at the rate of 10% per annum simple interest. The total interest received after 5 years is Rs 13300. What is the ratio of money lent at the rate of 24% and 10%?

Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ?