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
If the ratio of three numbers A, B and C is 2 ∶ 3 ∶ 5, and the sum of the squares of these numbers is 3800, then the value of C is:
A bag contains ₹310 in the form of 5 rupee, 2 rupee and 1 rupee coins in the ratio 4 ∶ 3 ∶ 5. What is the number of 5 rupee coins?
The ratio of three numbers is 3 ∶ 5 ∶ 4 and the sum of their squares is 11250. Find the sum of the numbers.
When 'x' is subtracted from each of the numbers 22, 39, 56 and 107, then the resulting numbers, in this order, are in proportion. What is the mean proportional between (x + 3) and (3x - 7)?
The salaries of Ravi and Sumit are in the ratio 4 ∶ 5. If the salary of each is increased by Rs. 6,000 the new ratio becomes 35 ∶ 40. What will be Sumit's increased salary?
