Question
Download Solution PDFThe average salary of employees in three departments P, Q and R in the company is ₹ 85,000, ₹ 75,000 and ₹ 83,000 respectively. If the average salary of department P and Q is ₹79,000 and the average salary of department Q and R is ₹80,000, then what will be the average salary of the three departments?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Average salary of department P = ₹85,000
Average salary of department Q = ₹75,000
Average salary of department R = ₹83,000
Average salary of departments P and Q = ₹79,000
Average salary of departments Q and R = ₹80,000
Formula used:
Average salary = (Total salary of the department) / (Number of employees)
Calculation:
Let the number of employees in department P be Pn, in department Q be Qn, and in department R be Rn.
For departments P and Q, the combined average salary is ₹79,000, so:
⇒ (Pn × ₹85,000 + Qn × ₹75,000) / (Pn + Qn) = ₹79,000
⇒ Pn × ₹85,000 + Qn × ₹75,000 = ₹79,000 × (Pn + Qn)
⇒ Pn × ₹85,000 + Qn × ₹75,000 = ₹79,000 × Pn + ₹79,000 × Qn
⇒ Pn × ₹85,000 - ₹79,000 × Pn = ₹79,000 × Qn - Qn × ₹75,000
⇒ Pn × ₹6,000 = ₹4,000 × Qn
⇒ Pn /Qn = ₹4,000/₹6,000 = 2/3
Similarly, for departments Q and R, the combined average salary is ₹80,000, so:
⇒ (Qn × ₹75,000 + Rn × ₹83,000) / (Qn + Rn) = ₹80,000
⇒ Qn × ₹75,000 + Rn × ₹83,000 = ₹80,000 × (Qn + Rn)
⇒ Qn × ₹75,000 + Rn × ₹83,000 = ₹80,000 × Qn + ₹80,000 × Rn
⇒ ₹80,000 × Qn - Qn × ₹75,000 = Rn × ₹83,000 - ₹80,000 × Rn
⇒ Qn × ₹5,000 = Rn × ₹3,000
⇒ Qn/Rn = ₹3,000/₹5,000 = 3/5
On simplifying the ratio we get,
Pn : Qn : Rn = 2 : 3 : 5
Let’s simplify the total average salary of all three departments:
⇒ The total salary of all three departments = (Pn × ₹85,000) + (Qn × ₹75,000) + (Rn × ₹83,000)
⇒ (2 × ₹85,000) + (3 × ₹75,000) + (5 × ₹83,000)
⇒ ₹1,70,000 + ₹2,25,000 + ₹4,15,000 = 8,10,000
Average salary of the three departments = 8,10,000/(2 + 3 + 5) = 81000
∴ The average salary of the three departments will be ₹81,000.
Last updated on May 26, 2025
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