Two numbers are in the ratio 5:7. If 9 is added to each, the new ratio becomes 8:11. What are the original numbers?
135 and 189
Let the two numbers be \(5x\) and \(7x\), since they are in the ratio 5:7.
Adding 9 to each gives the new ratio: \(\frac{5x+9}{7x+9} = \frac{8}{11}\).
Cross-multiply: \(11(5x+9) = 8(7x+9)\), i.e. \(55x + 99 = 56x + 72\).
Solve: \(99 - 72 = 56x - 55x\), so \(x = 27\).
The numbers are \(5x = 5\times 27 = 135\) and \(7x = 7\times 27 = 189\).
Hence, the original numbers are 135 and 189.
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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:
