Raja drives North 25 km. He then turns right and travels 2 km and then turns right and drives another 25 km. How far does he have to travel to get back to the starting point?

Solution
If CP = ₹ 20, % loss = 25% then SP =?

Solution
\(S.P.= C.P \frac{C.P\times Loss%}{100}\)
\(=20\frac{20\times 25}{100}=15\)
A cistern is filled in 9 hours but it takes 10 hours to fill when there is a leak in its bottom. If the cistern is full, in what time shall the leak empty it?

Solution
\(\Rightarrow \frac{1}{9}\frac{1}{x}=\frac{1}{10}\)
\(\Rightarrow \frac{1}{x}=\frac{1}{9}\frac{1}{10}=\frac{109}{90}=\frac{1}{90}\)
⇒x = 90 hours
Two sums of money are proportional to 8 : 13. If the first sum is ₹ 48, what is the addition of the two sums?

Solution
8x = 48
x=6
⇒21x = 21 × 6 = 126
The average age of 30 students in a class is 16 years. It the age of their teacher is 47 years, what is the average age of the students and teacher combined?

Solution
\(\frac{30\times 16+47\times 1}{30+1}\)
\(\frac{480+47}{31}=17\)
What percentage of 270 kg is 108 kg?

Solution
\(\Rightarrow \frac{270\times x}{100}=108\)
⇒x=40
In a library ^{1}⁄_{2} of the books are text books, ^{3}⁄_{4} of the remaining books are reference books and the remaining 150 books are encyclopaedias. Find out total number of books in the library.

Solution
Suppose the total number of books = x
\(\frac{x}{2}+\left ( \frac{x}{2}\times \frac{3}{4} \right )+150=x\)
\(\Rightarrow \frac{x}{2}+\frac{3x}{8}+\frac{150}{1}=x\)
\(\Rightarrow \frac{4x+3x+1200}{8}=x\)
⇒ax  7x = 1200
⇒x = 1200
Find the greatest number that will divide 148, 246 and 623 leaving remainders 4, 6 and 11 respectively

Solution
H.C.F = 12
Find the number that will exactly divide 200 and 300

Solution
\(\frac{200}{20}=10;\frac{300}{20}=15\)

Solution
\(\frac{16}{6}+\frac{33}{4}\frac{47}{8}\)
\(=\frac{76+198141}{24}\)
\(=\frac{274141}{24}=\frac{133}{24}\)