Question

Jaya has a certain number of word problems with her. She can solve some fixed number of problems every hour. After solving for 6 hours, she is left with 384 problems. If she solves for 12 hours, she will be left with 144 problems. Find the number of word problems Jaya is left with after 8 hours of solving.

• A. 38
• B. 624
• C. 40
• D. 304

Answer 1

The correct option is D

304

Let the number of word problems solved in one hour be $x$.
Now,
After solving for 6 hours,
Number of word problems solved = $6\times x$
Number of word problems left = $384$
$\therefore$ Total number of word problems = $6x+384$$\dots$(i)
After solving for 12 hours,
Number of word problems solved = $12\times x$
Number of word problems left = $144$
$\therefore$ Total number of word problems = $12x+144$$\dots$(ii)
Since the total number of word problems are the same we can equate (i) and (ii)
$\Rightarrow$$6x+384=12x+144$
$\Rightarrow$$6x=240$
$\Rightarrow$$x=40$.
$\therefore$ Total number of word problems Jaya has to solve = $40\times 6+384=624$.
In 8 hours, Jaya can solve $40\times 8$ = 320 word problems.
$\therefore$ Total number of word problems Jaya is left with after 8 hours of solving = $624-320=304$.