To interpret this question on Interest, I would take the help of ratios instead of the more common approach of using decimals or fractions.
From the question data, we know that the annual rate of interest of investment B is 1 ½ times that of investment A. Let x be the annual rate of interest of A and y be the corresponding value for B.
From the data given, y = \(\frac{3}{2}\) x or in other words, \(\frac{x}{y}\) = \(\frac{2}{3}\). Since x and y are in the ratio of 2:3, we can assume x = 2k and y = 3k. Doing this is actually going to help us during the later stages of the solution.
From statement I alone, the interest for 1 year is $50 and $150 for investments A and B respectively. Since we know that SI = P*T*R/100, we can formulate equations for the 2 investments.
If we say the investment in A is a and the investment in B is b, we can say,
50 = \(\frac{a*2k}{100}\) and
150 = \(\frac{b*3k}{100}\). Solving the equations, we have,
a*k = 2500 and b*k = 5000. Since we do not know the value of k, we will not be able to calculate the value of a.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, the amount put into investment B is twice the amount put in investment A.
This is insufficient to find a unique value for the investment in A.
Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.
Combining the data given in statements I and II, we have the following:
From statement II, we know that the investment in B is twice the investment in A. Using this along with the data given in statement I, we can say b=2a.
Because of the above relationships, the equations will now become,
a*k = 2500 and
2a*k = 5000. These are a pair of dependent equations and insufficient to find out the unique value of a. (this is where the ratio method actually helped us because we were able to develop equations in terms of k)
The combination of statements is insufficient. Answer option C can be eliminated.
The correct answer option is E.
Hope that helps!
Arvind
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