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Laila12618
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In a startup there are 120 employees. The average age is 25. If the nu 02 Mar 2023, 06:17
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65% (hard)

Question Stats:

69% (03:25) correct 31% (03:19) wrong based on 165 sessions

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In a startup there are 120 employees. The average age is 25. If the number of female increased by half of its previous number and the number of males becomes 3/4th of its previous number, the total number of staff remains unchanged. The new average age is 22 years. Also it was observed that the average age of males and females remained unchanged. Find the average age of males now.

A. 25
B. 31
C. 13
D. 15
E. 23
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In a startup there are 120 employees. The average age is 25. If the nu 15 May 2025, 06:36
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Laila12618
In a startup there are 120 employees. The average age is 25. If the number of female increased by half of its previous number and the number of males becomes 3/4th of its previous number, the total number of staff remains unchanged. The new average age is 22 years. Also it was observed that the average age of males and females remained unchanged. Find the average age of males now.

A. 25
B. 31
C. 13
D. 15
E. 23

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You can solve it in 15 seconds (due to the answer choices):

The average age in both groups is unchanged. The average age of males is higher (when their proportion decreases, the new average of males and females drops). So, the age of males must be higher than 25 (because there are also females who decrease the average in the first start-up team). So, the only suitable option among the answer choices is B.
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In a startup there are 120 employees. The average age is 25. If the nu 02 Mar 2023, 17:44
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Laila12618
In a startup there are 120 employees. The average age is 25. If the number of female increased by half of its previous number and the number of males becomes 3/4th of its previous number, the total number of staff remains unchanged. The new average age is 22 years. Also it was observed that the average age of males and females remained unchanged. Find the average age of males now.

A. 25
B. 31
C. 13
D. 15
E. 23

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Number of male employees = 4y
Number of female employees = 2x

4y + 2x = 120

2y + x = 60 --------- (1)

If the number of female increased by half of its previous number and the number of males becomes 3/4th of its previous number, the total number of staff remains unchanged

Number of male employees = \(4y * \frac{3}{4}\) = 3y
Number of female employees =\( 2x + (\frac{2x}{2})\) = 3x

3x + 3y = 120

x + y = 40 --------- (2)

Subtracting equation (2) from equation (1) we get

y = 20 ; x = 20

Therefore

The original number of males = 80
The original number of females = 40

The new number of males = 60
The new number of females = 60

Let's assume

  • the average age of males = m
  • the average age of females = f

In a startup there are 120 employees. The average age is 25

80m + 40f = 120 * 25

Dividing by 40 into both sides

2m + f = 75 -------- (3)

The new average age is 22 years. Also it was observed that the average age of males and females remained unchanged

60m + 60f = 120 * 22

Dividing by 60 into both sides

m + f = 44 -------- (4)

Subtracting equation (4) from equation (3) we get

m = 75 - 44 = 31

The average age of males = 31
The average age of females = 13

Option B

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Note: The answer is indicated as C, which I believe is incorrect.
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In a startup there are 120 employees. The average age is 25. If the nu 15 Mar 2023, 02:03
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Laila12618
In a startup there are 120 employees. The average age is 25. If the number of female increased by half of its previous number and the number of males becomes 3/4th of its previous number, the total number of staff remains unchanged. The new average age is 22 years. Also it was observed that the average age of males and females remained unchanged. Find the average age of males now.
A. 25
B. 31
C. 13
D. 15
E. 23
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Solution:

  • Let number of male and female employees be m and f respectively
  • So initially we had \(m+f=120.....(i)\)
  • After which we had \(\frac{3m}{4}+\frac{3f}{2}=120\) or \(m+2f=160.....(ii)\)
  • Solving equation i and ii we get \(f=40\) and \(m=80\)

  • Average age in first scenario = 25
  • We can write \(m*a_m+f*a_f=25\times 120\) where \(a_m\) and \(a_f\) are average ages of male and female respectively
    \(⇒80a_m+40a_f=3000\)
    \(⇒2a_m+a_f=75.....(iii)\)

  • Average age in first scenario = 21
  • We can write \(\frac{3m}{4}*a_m+\frac{3f}{2}*a_f=21\times 120\)
    \(⇒60a_m+60a_f=2640\)
    \(⇒a_m+a_f=44.....(iv)\)

  • Solving equations iii and iv together we get \(a_m=31\)


Hence the right answer is Option B
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In a startup there are 120 employees. The average age is 25. If the nu 27 Feb 2026, 03:55
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Deconstructing the Question

There are 120 employees with initial average age 25, so total initial age sum is \(120\cdot 25=3000\).

Let initial males be M, initial females be F, with \(M+F=120\).
Females increase by half, so \(F'=\frac{3}{2}F\).
Males become three-fourths, so \(M'=\frac{3}{4}M\).
Total remains 120, so \(\frac{3}{2}F+\frac{3}{4}M=120\).

Let male average age be a and female average age be b. These averages stay unchanged.
New overall average is 22, so new total age sum is \(120\cdot 22=2640\).

Step-by-step

From \(M+F=120\), write \(M=120-F\) and substitute into \(\frac{3}{2}F+\frac{3}{4}M=120\):

\(\frac{3}{2}F+\frac{3}{4}(120-F)=120\)

\(\frac{3}{2}F+90-\frac{3}{4}F=120\)

\(\frac{3}{4}F=30\)

\(F=40\)

Then \(M=80\), so \(F'=\frac{3}{2}\cdot 40=60\) and \(M'=\frac{3}{4}\cdot 80=60\).

Use weighted averages with constant group means:

Initial: \(80a+40b=3000\)
New: \(60a+60b=2640\) so \(a+b=44\)

Divide the initial equation by 40: \(2a+b=75\)
Substitute \(b=44-a\):

\(2a+(44-a)=75\)

\(a=31\)

Answer: B
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