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 total number of word problems Jaya has to solve.

• A. 318
• B. 624
• C. 640
• D. 504

Answer 1

The correct option is B

624

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 = $40\times 6+384=624$.