Question

A factory produces blue and red pens at the rate given in the table. The missing entries are

• A. A = 5 ; B = 20
• B. A = 6 ; B = 24
• C. A = 5 ; B = 25
• D. A = 6 ; B = 20

Answer 1

The correct option is D A = 6 ; B = 20

The ratio of red pens to blue pens in batch 1 = 2:5

$\frac{2}{5}=2:5$

Similarly, for batch 2, we have:

$\frac{4÷2}{10÷2}=\frac{2}{5}=2:5$

Any ratio a:b can be written in its fractional form as:

$a:b=\frac{a}{b}$
$\therefore 2:5=\frac{2}{5}$

Multiplying the numerator and the denominator by 3, we get:

$\frac{2\times 3}{5\times 3}=\frac{6}{15}=\frac{\text{Red pens in batch 3}}{\text{Blue pens in batch 3}}$

So, when the number of blue pens is 15, the number of red pens will be 6.

Hence, A = 6

Similarly, multiplying the numerator and denominator of the fraction by 4, we get:

$\frac{2\times 4}{5\times 4}=\frac{8}{20}=\frac{\text{Red pens in batch 4}}{\text{Blue pens in batch 4}}$

So, when the number of red pens is 8, the number of blue pens will be 20.

Hence, B = 20