The ratio of hard and easy questions in an exercise is $2 : 5$ . How many hard questions does the exercise have if there are $49$ questions in all ?

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Solution

Since ,the ratio of hard and easy questions in an exercise is $2 : 5$ .
Therefore, let the number of hard and easy questions be $2 x$ and $5 x$ respectively.
so, the total number of questions $=$ Hard questions + easy questions
$= 2 x + 5 x$
$= 7 x$
Since ,the total number of questions $= 49$
Therefore, $7 x = 49$
$x = \frac{49}{7} = 7$ .
Therefore, total number of hard questions $= 2 x = 2 \times 7 = 14 .$
Hence ,number of hard questions $= 14$ .

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The ratio of hard and easy questions in an exercise is 2:5. How many hard questions does the exercise have if there are 49 questions in all ?

The ratio of hard and easy questions in an exercise is $2 : 5$ . How many hard questions does the exercise have if there are $49$ questions in all ?