Quartiles of a grouped frequency

For the set of data given below find or estimate, as appropriate, the quartiles.

Class| 1-9 | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69

Frequency| 3 | 6 | 12 | 18 | 10 | 4 | 2

**Here is my work**

Cumulative frequency| 3 | 9 | 21 | 39 | 49 | 53 | 55

Since n=55

So: Q₁ = b + {(¼ n – f)/fc} * c

= 19.5 + {(1/4 (55) – 9)/12} * 9 = 23.06

And Q₃ = 39.5 +{( ¾(55) – 39)/10} * 9 = 41.53

So my answers are **Q₁ = 23.06 & Q₃ = 41.53**

For this question, is it necessary to work for Q2? So far I know Q2 is median.

There is another problem; my answers are not accurate as per my book’s answer. It says **23.46 & 41.75**. So where is the problem? Please help me.