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 had kept solving for 12 hours, she would have been 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

Jaya can solve a fixed number of word problems per hour. Let that value be $x$ word problems per hour.
Now,
After solving for 6 hours,
Number of word problems solved = $6\times x$
Number of word problems left = $384$
Total number of word problems = $6x+384$$\dots$(i)
After solving for 12 hours,
Number of word problems solved = $12\times x$
Number of word problems left = $144$
Total number of word problems = $12x+144$$\dots$(ii)
Since the total number of word problems is the same, (i) = (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 = $624-320=304$.