In 2010, a library contained a total of 11500 books in two categories - fiction and non-fiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

$6600$

$6160$

$5500$

$6000$

✅ Correct Option: 1

We can see we're dealing with a system of equations involving percentage increases.

Let's define our variables clearly:

Let $x$ = number of fiction books in 2010

Let $y$ = number of non-fiction books in 2010

The problem statement seems to be missing the total for 2010, but from the context and solution, it should be 11500 books.

When something increases by 10%, the new amount becomes 110% of the original, which we write as 1.1 times the original. Similarly, a 12% increase means 1.12 times the original.

From the given information:

Total books in 2010: $x + y = 11500$

Total books in 2015: $1.1x + 1.12y = 12760$

The first equation by 1.1:

$1.1x + 1.1y = 12650$

Subtract this from the second equation:

$(1.1x + 1.12y) - (1.1x + 1.1y) = 12760 - 12650$

$0.02y = 110$

When we subtract, the $1.1x$ terms cancel out, leaving us with just the $y$ terms. This is a clever way to eliminate one variable quickly.

$y = \frac{110}{0.02} = 5500$

Using the first equation:

$x = 11500 - 5500 = 6000$

Fiction books in 2015:

$1.1 \times 6000 = 6600$

There were 6600 fiction books in the library in 2015.

When dealing with percentage change problems, always convert percentages to decimals (10% increase = multiply by 1.1) and look for opportunities to eliminate variables by strategic multiplication and subtraction.

CAT 2023 Slot 3

The population of a town in $2020$ was 100000. The population decreased by $y \%$ from the year $2020$ to 2021, and increased by $\mathrm{x} \%$ from the year $2021$ to 2022, where x and y are two natural numbers. If population in $2022$ was greater than the population in $2020$ and the difference between $x$ and $y$ is 10, then the lowest possible population of the town in $2021$ was

CAT 2020 Slot 3

In the final examination, Bishnu scored $52 \%$ and Asha scored $64 \%$ . The marks obtained by Bishnu is $23$ less, and that by Asha is $34$ more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored $84 \%$ , is

CAT 2021 Slot 3

In a tournament, a team has played $40$ matches so far and won $30 \%$ of them. If they win $60 \%$ of the remaining matches, their overall win percentage will be $50 \%$ . Suppose they win $90 \%$ of the remaining matches, then the total number of matches won by the team in the tournament will be

CAT 2019 Slot 1

The income of Amala is $20 \%$ more than that of Bimala and $20 \%$ less than that of Kamala. If Kamala's income goes down by $4 \%$ and Bimala's goes up by $10 \%$ , then the percentage by which Kamala's income would exceed Bimala's is nearest to

CAT 2020 Slot 1

In a group of people, $28\%$ of the members are young while the rest are old. If $65\%$ of the members are literates, and $25\%$ of the literates are young, then the percentage of old people among the illiterates is nearest to

CAT 2019 Slot 2

In an examination, the score of $A$ was $10\%$ less than that of $B$ , the score of $B$ was $25\%$ more than that of $C$ , and the score of $C$ was $20\%$ less than that of $D$ . If A scored $72$ , then the score of $D$ was

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)