Quantitative Aptitude Test - 4

Statement I:

Total profit = 27500 Rs

Statement II:

Seema's investment = 25000 Rs

Sarita's investment = 32000 Rs

Statement I and II both are not sufficient to give the answer.

Given:

The ratio of capitals invested by A, B and \(C=2: 3: 5\)

The ratio of months for which they invested \(=4: 2: 3\)

The difference between the profit shares of A and B = Rs. \(1,86,000\)

Formula used:

Profit = Time × Money

The ratio of profit of A, B and C \(=(2 \times 4):(3 \times 2):(5 \times 3)\)\(=8: 6: 15\)

According to the question,

\(\Rightarrow(8 x-6 x)=\) Rs. \(1,86,000\)

\(\Rightarrow 2 x=\) Rs. \(1,86,000\)

\(\Rightarrow x=\) Rs. \(93,000\)

Now, the C's share of profit \(=\) Rs. \((15 \times 93,000)\)

\(=\) Rs. \(13,95,000\)

\(\therefore\) The required share of C is \(13,95,000\).

Given:

Monthly incomes of \(A\) and \(B\) are in the ratio \(=3: 5\)

The ratio of their savings \(=2: 3\)

The income of \(B=3 \times\) Savings of A

As we know,

Income \(=\) Savings \(+\) Expenditure

Let the monthly income of \(A\) and \(B\) be 300 and 500 and the savings be \(2 x\) and \(3 x\) respectively

\(\Rightarrow 500=3 \times 2 x\)

\(\Rightarrow 500=6 x\)

\(\Rightarrow x=\frac{250}{3}\)

Expenditure of \(A=\) Income of \(A-\) Savings of \(A\)

\(=300-2 \times\left(\frac{250}{3}\right)\)

\(=\frac{(900-500)}{3}\)

\(=\frac{400}{3}\)

Expenditure of \(B=\) Income of \(B-\) Savings of \(B\)

\(=500-3 \times\left(\frac{250}{3}\right)\)

\(=500-250\)

\(=250\)

Ratio of expenditure of \(A\) and \(B=\frac{\left(\frac{400}{3}\right)}{250}\)

\(=\frac{400}{750}\)

\(=\frac{8}{15}\)

\(\therefore\) The ratio of the expenditures of \(A\) and \(B\) is \(8: 15\).

Here, The average age of eleven cricket players \(=20\) years

Total age of 11 players \(=11 \times 20=220\) years

If the age of the coach is also included, the average age increases by \(10 \%\)

i.e. Total increase average \(=20\) of \(10 \%=2\)

New average of 11 players and the coach \(=20+2=22\) years

Total age of 11 players and the coach \(=12 \times 22=264\) years

\(\therefore\) Age of the coach \(=(264-220)\) years \(=44\) years

Total run made by Mohan \(=44+53+26+22+38=183\)

Average run \(=\frac{183}{5}=36.60\)

A consistent good batsman is one whose average is good and who never scored zero in 5 innings

Total run made by Kishor\(=72+56+48+63+51=290\)

Average of Kishor\(=\frac{290 }{5}=58\)

Total run made by Chetan \(=32+135+0+182+0=349\)

Average of Chetan \(=\frac{349}{5}=69.8\)

But Chetan scored two zeros and Kishor scored none.

Average of Kishor is higher than Anand, Ramesh and Mohan and he was consistent throughout his 5 innings with no Zeros is any inning.

∴ Kishor is the consistent good batsman.

Total run made by Chetan \(=32+135+0+182+0=349\)

We see that Chetan scored highest runs but he also scored 2 zeros which more than others.

Total run made by Ramesh \(= 9 + 11 + 17 + 6 + 10 = 53\)

The run made by Ramesh was consistently poor if we compare form others, He scored the lowest runs.

Total run made by Mohan \(=44+53+26+22+38=183\)

Total run made by Anand \(=22+15+42+13+0=92\)

Total run made by Kishor \(=72+56+48+63+51=290\)

Total run made by Chetan \(=32+135+0+182+0=349\)

Total run made by Ramesh \(=9+11+17+6+10=53\)

\(\therefore\) Highest run was made by Chetan i.e., \(349\).

Every student is learning at least one language. Hence there is no one who fall in the category ‘neither’.

So in this case, n(EUF) = n(U).

It is mentioned in the problem that a total of 18 are learning English. This DOES NOT mean that 18 are learning ONLY English. Only when the word ‘only’ is mentioned in the problem should we consider it so.

Now, 18 are learning English and 8 are learning both. This means that 18 – 8 = 10 are learning ONLY English.

n(U) = 30, n(E) = 10

n(EUF) = n(E) + n(F) – n(E∩F)

30 = 18+ n(F) – 8

n(F) = 20

Therefore, total number of students learning French = 20.

Finally, the Venn diagram looks like this.