Question
Download Solution PDFThere are Senior officers and Secretaries in an office. If 15 Secretaries went on leave, then every Secretary has two Senior officers. After that 45 Senior officers went on leave and now every Senior officer has 5 Secretaries. Then find out how many Secretaries were there initially.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
There are Senior officers and Secretaries in an office.
If 15 Secretaries went on leave, then every Secretary has two Senior officers.
After that, 45 Senior officers went on leave, and now every Senior officer has 5 Secretaries.
Formula used:
Let the initial number of Secretaries be S and the initial number of Senior officers be O.
After 15 Secretaries went on leave, every remaining Secretary has 2 Senior officers:
O = 2(S − 15)
After 45 Senior officers went on leave, every remaining Senior officer has 5 Secretaries:
S = 5(O − 45)
Calculation:
O = 2(S − 15)
⇒ O = 2S − 30
S = 5(O − 45)
⇒ S = 5(2S − 30 − 45)
⇒ S = 5(2S − 75)
⇒ S = 10S − 375
⇒ 375 = 9S
⇒ S = 375/9
⇒ S = 41.67
Since the number of Secretaries must be an integer, and 41.67 is close to 40, we round down:
⇒ S = 40
∴ The correct answer is option (4).
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