Two bags contain marbles in the ratio 5 : 7. If 12 marbles are transferred from the second bag to the first bag, the ratio of marbles in the two bags becomes 7 : 5. Find the original number of marbles in the second bag.
42
Let the original numbers of marbles be \(5x\) in the first bag and \(7x\) in the second bag.
After transferring 12 marbles from the second to the first, the counts become \(5x + 12\) and \(7x - 12\), and their ratio is 7 : 5.
Set up the equation \(\frac{5x + 12}{7x - 12} = \frac{7}{5}\) and cross-multiply: \(5(5x + 12) = 7(7x - 12)\).
Expand: \(25x + 60 = 49x - 84\), so \(144 = 24x\) and \(x = 6\).
The original number in the second bag is \(7x = 7 \times 6 = 42\).
Hence, the second bag originally had 42 marbles.
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Important Questions from Ratio and Proportion
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?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
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:
