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.
5
Let the original counts be R = 3k, B = 4k, G = 6k for some constant k.
After adding the marbles, the new counts are 3k + 20, 4k + 15, and 6k + x, where x is the number of green marbles added.
Step 1 – use the new red : blue ratio = 4 : 5:
\(\dfrac{3k+20}{4k+15} = \dfrac{4}{5}\)
\(5(3k+20) = 4(4k+15) \implies 15k + 100 = 16k + 60 \implies k = 40\)
Step 2 – substitute k = 40: R = 120, B = 160, G = 240. After adding: 140 red, 175 blue, (240 + x) green.
Step 3 – use the new blue : green ratio = 5 : 7:
\(\dfrac{175}{240 + x} = \dfrac{5}{7} \implies 7 \times 175 = 5(240 + x) \implies 1225 = 1200 + 5x \implies x = 5\)
Hence 5 green marbles were added.
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In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
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The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
