The number of red, blue, and green marbles in a bag is in the ratio 3 : 4 : 6. If 20 red marbles, 15 blue marbles, and an unknown…

Question

The number of red, blue, and green marbles in a bag is in the ratio 3 : 4 : 6. If 20 red marbles, 15 blue marbles, and an unknown number of green marbles are added to the bag, the ratio of red, blue, and green marbles becomes 4 : 5 : 7. Determine the number of green marbles added.

1. A. 3
2. B. 5 (Correct answer)
3. C. 7
4. D. 9

Correct Answer

Option B — 5

Detailed Solution & Explanation

The correct answer is 5.

Key Points

• Let the original counts be 3k, 4k and 6k.
• Use the red and blue parts first, since both additions are known: $(3k + 20) : (4k + 15) = 4 : 5$ gives $15k + 100 = 16k + 60$, so k = 40.
• Red becomes 140 and blue 175, so one part of the new ratio is $140 \div 4 = 35$. Green must finish at $7 \times 35 = 245$, and it began at $6 \times 40 = 240$.
• Green marbles added = 245 − 240 = 5.

Additional Information

• Choose the two quantities whose changes are fully known — that reduces two unknowns to one and avoids simultaneous equations.
• Always check the result against a part of the ratio you did not use to derive it; here 140 : 175 : 245 does simplify to 4 : 5 : 7.
• Introducing a common multiplier k is the standard first move whenever a ratio is given without absolute values.

प्रश्न (हिन्दी में)

एक बैग में लाल, नीले और हरे मार्बल की संख्या का अनुपात 3 : 4 : 6 है। यदि बैग में 20 लाल मार्बल, 15 नीले मार्बल और अज्ञात संख्या में हरे मार्बल डाले जाएं, तो लाल, नीले और हरे मार्बल का अनुपात 4 : 5 : 7 हो जाता है। डाले गए हरे मार्बलों की संख्या ज्ञात कीजिए।

1. A. 3
2. B. 5
3. C. 7
4. D. 9