Question

Suppose Sheetal’s birthday is on the
P
th of October and Karthik’s birthday is on the
Q
th of November, where
P
and
Q
are perfect squares. If Sheetal was born 10 days before Karthik, then the value of
P
−
2
Q
will be __________

Answer 1

Step-by-step explanation:

The birth day of Sheela =P th of October

The birth day of Karthik=Q th of November

Here P and Q are perfect squares then

The birthday of Sheela may be 1,4,9,16,25 of October.

and

The birthday of Karthik may be 1,4,9,16,25 of

November.

The difference of their birthdays =10 days

so from that it is clearly

the birthday of Sheela =25 th October

Therefore,P=25

The birthday of Karthik =4 th November

Therefore, Q=4

(

since the difference of 4th November to 25 th October=10days

October has 31 days)

The value of P-2Q=25-2(4)=25-8=17

The value of P-2Q=17

Answer 2

Given,

Sheetal's birthday $\[ = Pth\,October\]$

Karthik's birthday $\[ = Qth\,November\]$

$\[Pth\,October - Qth\,November = 10days\]$

P and Q are perfect square.

Solution,

$\[Pth\,October - Qth\,November = 10days\]$-----------(1)

Perfect square in October month after 20th October $\[ = 25\,October\]$

Perfect square in November before 10th November, $\[ = 4th\,November,9th\,November\]$

According to first equation the number of days should be equal to 10. So 4th November satisfy the given condition.

Calculate the value of $\[P - 2Q\]$

$\[\begin{array}{l} = Pth\,October - 2Qth\,November\\ = 25th\,October - 2 \times 4th\,November\\ = 14\,days\end{array}\]$

Hence the value is 14 days.