In a bag, the numbers of red marbles and blue marbles are in the ratio 9 : 4. Had there been 35 more blue marbles, the ratio would have been 9 : 11. What is the total number of marbles in the bag?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 65
Only the blue marbles change, so the number of red marbles stays the same in both ratios.
Red \(=9k\), blue \(=4k\)
\(\displaystyle \frac{9k}{4k+35}=\frac{9}{11}\)
\(99k=36k+315\), so \(63k=315\) and \(k=5\)
Total \(=9k+4k=13\times5=65\)
The bag has 65 marbles (45 red and 20 blue).