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Yesterday, a certain school had an equal number of boys and girls. Tod
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29 Dec 2025, 04:09
29 Dec 2025, 04:09
Expert Reply
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Question Stats:
66% (01:42) correct
33% (00:31) wrong based on 6 sessions
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Yesterday, a certain school had an equal number of boys and girls. Today, 18 boys left the school, and the ratio of the number of boys to girls is now 3 to 4 .
Quantity A |
Quantity B |
Number of boys in the school now |
72 |
- Part of the project: GRE Daily Quant Challenge - Topic-Wise 2025!!!
- Also replying to the unanswered questions
Re: Yesterday, a certain school had an equal number of boys and girls. Tod
[#permalink]
18 Jan 2026, 03:27
18 Jan 2026, 03:27
Expert Reply
To find the relationship between Quantity $A$ and Quantity $B$, we can set up an algebraic equation based on the changes in the school's population.
1. Define the Variables
- Let $x$ be the number of boys yesterday.
- Since the number of boys and girls was equal, there were also $x$ girls yesterday.
2. Set up the Equation for "Today"
Today, 18 boys left, but the number of girls remained the same.
- Boys today: $x-18$
- Girls today: $x$
We are told the new ratio of boys to girls is $3: 4$. We can write this as a proportion:
$$
\(\frac{x-18}{x}=\frac{3}{4}\)
$$
3. Solve for $x$ (The original number)
Cross-multiply to solve for $x$ :
$$
\(\begin{gathered}
4(x-18)=3 x \\
4 x-72=3 x
\end{gathered}\)
$$
$$
\(x=72\)
$$
So, there were $\(\mathbf{7 2}\)$ boys in the school yesterday.
4. Calculate Quantity A
Quantity A asks for the number of boys in the school now.
Boys now $\(=x-18\)$
Boys now $\(=72-18=\mathbf{5 4}\)$
1. Define the Variables
- Let $x$ be the number of boys yesterday.
- Since the number of boys and girls was equal, there were also $x$ girls yesterday.
2. Set up the Equation for "Today"
Today, 18 boys left, but the number of girls remained the same.
- Boys today: $x-18$
- Girls today: $x$
We are told the new ratio of boys to girls is $3: 4$. We can write this as a proportion:
$$
\(\frac{x-18}{x}=\frac{3}{4}\)
$$
3. Solve for $x$ (The original number)
Cross-multiply to solve for $x$ :
$$
\(\begin{gathered}
4(x-18)=3 x \\
4 x-72=3 x
\end{gathered}\)
$$
$$
\(x=72\)
$$
So, there were $\(\mathbf{7 2}\)$ boys in the school yesterday.
4. Calculate Quantity A
Quantity A asks for the number of boys in the school now.
Boys now $\(=x-18\)$
Boys now $\(=72-18=\mathbf{5 4}\)$
gmatclubot
Re: Yesterday, a certain school had an equal number of boys and girls. Tod [#permalink]
18 Jan 2026, 03:27
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