A company has two departments, ‘A’ and ‘B’, with employees in the ratio \(5:7\), respectively. If 28 employees are transferred from department ‘B’ to ‘A’, the ratio becomes \(1:1\). How many employees does each department have originally?
140 in A, 196 in B
Let the number of employees in A and B be \(5x\) and \(7x\) respectively.
After transferring 28 employees from B to A: \(5x + 28 = 7x - 28\).
Solving: \(2x = 56\), so \(x = 28\).
Employees in A \(= 5 \times 28 = 140\) and employees in B \(= 7 \times 28 = 196\).
Check: after transfer, A has \(140+28=168\) and B has \(196-28=168\), an equal ratio of \(1:1\).
Hence, department A originally has 140 employees and department B has 196 employees.
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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:
