CT 18: Linear Equation – II

1.If 1 is subtracted from the denominator of a fraction, it becomes 1/3, and if 1 is subtracted from the numerator, the fraction becomes 1. What is the fraction?

2. The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2 Then, the rational number is:

3. The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, the number is

4. Ram buys 4 chairs and 9 stools for Rs. 1340. If he sells chairs at 10% profit and stools at 20% profit, he earns a profit of Rs. 188. How much money did he have to pay for the chairs?

5. 5 pencils, 6 notebooks and 7 erasers cost Rs. 250; whereas 6 pencils, 4 notebooks and 2 erasers cost Rs. 180. What is the cost of 2 notebooks and 4 erasers ?

6. If 2a + 3b = 14 and 2a - 3b = 10, then find the value of ‘ab’.

7. Students of a class are made to sit in rows of equal number of chairs. If number of students is increased by 2 in each row, then the number of rows decrease by 3. If number of students is increased by 4 in each row, then the number of rows decreases by 5. What is the number of students in the class?

8. The sum of digits of a 2-digit number is 12. When the digits are reversed, the number becomes greater by eighteen. What is the difference between the digits in the number?

9. A number is larger than half of 100. It is more than 6 tens and less than 8 tens. The sum of its digits is 9. The tens digit is the double of the one's digit. What is the number?

10. The difference between a two-digit number and the number obtained by interchanging the digits is 54 and the sum of digits is 10. Find the average of both the two-digit numbers.