Quantitative Aptitude Test - 2

From the statement I, we can conclude the sum of money Rina had invested but nowhere it is mentioned the rate of interest Rina had invested her money. Therefore we can not reach theanswer by the statement alone.

From the statement II, Difference between CI and SI is Rs.12  at the end of 2 years. But as the principal is not given here, we can't deduce the rate of interest using statement II alone.

But, from the statement I, we concluded the sum of money and to this statement we can conclude the rate of interest.

Therefore, if we combine statement I and statement II then we can conclude that the rate of interest was 10% per annum and the sum of money was Rs. 1200 now we can calculate the amount Rina will receive al the end of 2 years

Therefore, the data in both the statements I and II together is necessary to answer the question.

In the question, the distance is given.

In the statement I, the ratio of speed is given.

From the statement I we can conclude that P’s speed : Q’s speed = 4 : 5  but we cannt find out speed of individual trains.

In statement II the average speed of both the trains is given so we cannot find out speed of individual trains.

If we combine statement I with statement II, then we can get as P’s speed = 40 km per hr Q’s speed = 50 km per hr

Therefore, the data in both the statements I and II is necessary to answer the question.

Given:

Shekhar's first investment \(=25000\)

Shekhar's second investment \(=35000\)

Shekhar's third investment \(=45000\)

Calculation:

Sekar : Rajeev : Jatin 

\(=\{(25000 \times 12)+(35000 \times 12)+(45000 \times 12)\}:(35000 \times 24):(35000 \times 12)\)

\(=1260000: 840000: 420000\)

\(=3: 2: 1\)

Rajeev's Share \(=150000 \times(\frac{2}{6})\)

\(\therefore\) Rajeev's Share \(=\) Rs. \(50000 \)

Given:

When\(x\) is added to each of \(9,15,21\) and 31 , the numbers so obtained are in proportion.

As we know,

If \(a, b, c\) and \(d\) are in proportion, then \(\frac{a}{b}=\frac{c}{d}\)

Mean proportion of two numbers \(a\) and \(b\) is \(\sqrt{a b}\)

According to Question,

\(\frac{(9+x)}{(15+x)}=\frac{(21+x)}{(31+x)}\)

\(\Rightarrow(9+x)(31+x)=(15+x)(21+x)\)

\(\Rightarrow x^{2}+40 x+279=x^{2}+36 x+315\)

\(\Rightarrow 4 x=36\)

\(\Rightarrow x=9\)

Mean proportion of \((3 x-2)\) and \((5 x+4)\)

\(=\sqrt{\{(3 \times 9-2)(5 \times 9+4)\}}\)

\(=\sqrt{(25 \times 49)}\)

\(=35\)

\(\therefore\) Mean proportional between the numbers \((3 x-2)\) and \((5 x+4)\) is 35 .

\(\because\) Average of 5 numbers \(=333\)

\(\therefore\) Sum of all 5 numbers \(=333 \times 5\)

\(=1665\)

\(\Rightarrow 235+2 x 5+x 35+63 x+116=1665\)

\(\Rightarrow 2 x 5+x 35+63 x=1665-235-116\)

\(\Rightarrow 2 \times 5+x 35+63 x=131\underline{4} \quad-(1)\)

\(\because\) We need 4 at the unit digit.

\(\therefore\) The sum of the unit digits of " \(2 \times 5+x 35+63 \times\) " should have 4 as its unit digit.

\(\therefore\) To make it 4 , we need to add ' 4 ' to it. \((5+5+4=1 \underline{4})\)

\(\Rightarrow x=4\)

Verify the value of ' \(x\) ' by putting it in the equation (1)

\(\Rightarrow 245+435+634=1314\)

\(\therefore(x+1)+(x+8)+(x+3)=5+12+7\)

\(=24\)

\(\therefore\) Average of \(x+1, x+3\) and \(x+8\)

\(=\frac {24} {3}\)

\(=8\)

The ratio of imports to exports for the years 1998 and 1999 are \(1.25\) and \(1.40\) respectively.

Let the exports in the year \(1998=\) Rs. \(x\) crores.

Then, the exports in the year \(1999=\) Rs. \((500-x)\) crores.

\(\therefore 1.25=\frac{250}{x}\)

\(\Rightarrow x=\frac{250}{1.25}\)

\(=200 \quad\) [Using ratio for \(1998\)]

Thus, the exports in the year \(1999\)

\(=\) Rs. \((500-200)\) crores

\(=\) Rs. \(300\) crores.

Let the imports in the year \(1999=\) Rs. \(y\) crores.

Then, \(1.40=\frac{y}{300}\)

\(\Rightarrow y=(300 \times 1.40)\)

\(=420\)

\(\therefore\) Imports in the year \(1999=\) Rs. \(420\) crores.

The imports are minimum proportionate to the exports implies that the ratio of the value of imports to exports has the minimum value.

Now, this ratio has a minimum value \(0.35\) in \(1997\), i.e., the imports are minimum proportionate to the exports in \(1997\).

The graph gives only the ratio of imports to exports for different years. To find the percentage increase in imports from \(1997\) to \(1998\), we require more details such as the value of imports or exports during these years.

So, the data is inadequate to answer this question.

Given:

Imports of the company in \(1996=\) Rs. \(272\) crores

Ratio of imports to exports in the year \(1996=0.85\)

Let the exports in \(1996=\) Rs. \(x\) crores.

Then,

\(\frac{272}{x}=0.85\)

\(\Rightarrow x=\frac{272}{0.85}\)

\(\Rightarrow x=320\)

\(\therefore\) Exports in \(1996=\) Rs. \(320\) crores.

The exports are more than the imports implies that the ratio of the value of imports to exports is less than \(1\). Now, this ratio is less than \(1\) in the years \(1995, 1996, 1997,\) and \(2000\). Thus, there are four such years.