Question

$70$% of the total houses in the neighbourhood contains garden and $50$% among them contains $2$ gardens. If there are $26$ houses with $2$ gardens, then how many houses do not have garden?

• A. $22$
• B. $52$
• C. $74$
• D. $54$

Answer 1

The correct option is A $22$

Let the total number of houses be $x$.

Then, $0.7x$ contain garden.

And $0.5\times \left(0.7x\right)$ contain $2$ gardens.

Hence $0.5\times 0.7x=26$

$\frac{0.7x}{2}=26$ or $0.7x=52$

Now the number of houses without a garden is $30\%$ of the total number of houses.

But we know that $x=\frac{52}{0.7}$

Hence $0.3x=\frac{0.3}{0.7}\times 52=\frac{3}{7}\times 52=22$ (approx)