Question

What is the ratio of the quarter past 6 and 10 minutes to 7?

Answer 1

Hint: To solve this question, we should have knowledge of the reading clock, that is when the minute hand is before 6, then we use the word past and if the minute hand is between 6 and 12, then we use the word ‘to’. For example, 2:20 is called 20 minutes past 2 and 2:50 is called 10 minutes to 3.

Complete Step-by-Step solution:
In the question, we have to find the ratio of the quarter past 6 and 10 minutes to 7. For that, we should know what ‘past’ and ‘to’ means while reading the time on the clock. Here, ‘past’ means the time which has passed, and ‘to’ means the time which is remaining. So, we can say that quarter past 6 is nothing but 15 minutes has passed after 6 whereas 10 minutes to 7 depicts that 10 minutes are remaining to 7. We can write them as 6:15 and 6:50 respectively.
Here, we have to find the ratio of the time, so we will convert 6 hours 15 minutes and 6 hours 50 minutes into hours only. So, we will get,
6 hours 15 minutes = $$6+{\displaystyle \frac{15}{60}}hours$$
6 hours 50 minutes = $$6+{\displaystyle \frac{50}{60}}hours$$
Now, we will simplify it, so we will get,
$$6+{\displaystyle \frac{15}{60}}=6+{\displaystyle \frac{1}{4}}$$ and $$6+{\displaystyle \frac{50}{60}}=6+{\displaystyle \frac{5}{6}}$$
$$6+{\displaystyle \frac{15}{60}}={\displaystyle \frac{24+1}{4}}$$ and $$6+{\displaystyle \frac{50}{60}}={\displaystyle \frac{36+5}{6}}$$
$$6+{\displaystyle \frac{15}{60}}={\displaystyle \frac{25}{4}}$$ and $$6+{\displaystyle \frac{50}{60}}={\displaystyle \frac{41}{6}}$$
Therefore, 6 hours 15 minutes can be written as $${\displaystyle \frac{25}{4}}$$ hours and we can write 6 hours 50 minutes as $${\displaystyle \frac{41}{6}}$$ hours.
So, the ratio of 6 hours 15 minutes and 6 hours 50 minutes is
$$={\displaystyle \frac{{\displaystyle \frac{25}{4}}}{{\displaystyle \frac{41}{6}}}}$$
$$={\displaystyle \frac{25}{4}}\times {\displaystyle \frac{6}{41}}$$
$$={\displaystyle \frac{75}{82}}$$
Therefore, we can say that the ratio of quarter past 6 and 10 minutes to 7 is $${\displaystyle \frac{75}{82}}$$.

Note: In this question, the possible mistake one can make is by writing 6 hours 15 minutes as 6:15 and 6 hours 50 minutes as 6:50. Because 1 hour is equal to 60 minutes. So, while converting minutes to hours we have to divide minutes by 60.