Question

A choir is singing at a festival. On the first night $12$ choir members were absent so the choir stood in $5$ equal rows. On the second night only $1$ member was absent so the choir stood in $6$ equal rows. The same member of people stood in each row each night. How many members are in the choir?

• A. $65$
• B. $67$
• C. $70$
• D. $64$

Answer 1

Answer: (B)

$67$

Let $x$ be the number in choir

$1^{st}$ night in a row $=$ $2^{nd}$ night in a row

$\frac{x-12}{5}=\frac{x-1}{6}$

On cross multiplying, we get

$6(x-12)=5(x-1)$

$\Rightarrow 6x-72=5x-5$

$\Rightarrow 6x-5x=-5+72$

$\Rightarrow x=67$

Thus there are $67$ members in the choir.