2.The sum of a two digit number and the number obtained by reversing the digits is 66. If thedigits of the number differ by 2, find the number. How many such numbers are there?
3. The larger of two supplementary angles exceeds the smaller by 18°. Find the angles.
4. The taxi charges in Hyderabad are fixed, along with the charge for the distance covered.Upto first 3 km you will be charged a certain minimum amount. From there onwards youhave to pay additionally for every kilometer travelled. For the first 10 km, the charge paidis `166. For a journey of 15 km. the charge paid is `256. i. What are the fixed charges and charge per km? ii. How much does a person have to pay for travelling a distance of 25 km?
5. A fraction will be equal to 45 if 1 is added to both numerator and denominator. If, however,5 is subtracted from both numerator and denominator, the fraction will be equal to 12.What is the fraction?
6. Places A and B are 100 km apart on a highway. One car starts from A and another from Bat the same time at different speeds. If the cars travel in the same direction, they meet in 5hours. If they travel towards each other, they meet in 1 hour. What are the speeds of thetwo cars?
7. Two angles are complementary. The larger angle is 3° less than twice the measure of thesmaller angle. Find the measure of each angle.
8. A dictionary has a total of 1382 pages. It is broken up into two parts. The second part of thebook has 64 pages more than the first part. How many pages are in each part of the book?
9. A chemist has two solutions of hydrochloric acid in stock. One is 50% solution and theother is 80% solution. How much of each should be used to obtain 100ml of a 68%solution.
10. You have `12,000/- saved amount, and wants to invest it in two schemes yielding 10%and 15% interest. How much amount should be invested in each scheme so that youshould get overall 12% interest.
4.4 EQUATIONS REDUCIBLE TO A PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Now we shall discuss the solution of pairs of equations which are not linear but can bereduced to linear form by making suitable substitutions. Let us see an example: Example-12. Solve the following pair of equations.2 3+ = 13x y5 4- = -2x y Solution : Observe the given pair of equations. They are not linear equations. (Why?)