In a box, the numbers of solid-coloured balls and striped balls are in the ratio 7 : 2. Had there been 27 more striped balls, the ratio would have been 11 : 7. What is the total number of balls in the box?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 99
Only the striped balls change, so the number of solid-coloured balls stays the same in both ratios.
Solid \(=7k\), striped \(=2k\)
\(\displaystyle \frac{7k}{2k+27}=\frac{11}{7}\)
\(49k=22k+297\), so \(27k=297\) and \(k=11\)
Total \(=7k+2k=9\times11=99\)
The box has 99 balls (77 solid-coloured and 22 striped).