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163 Rh 10. Four times B's age exceeds A's age by twenty years, and one-third of A's age is less than B's age by two years: find their ages.

11. One-eleventh of A's age is greater by two years than one-seventh of B's, and twice B's age is equal to what A's age was thirteen years ago : find their ages.

12. In eight hours A walks twelve miles more than B does in seven hours; and in thirteen hours B walks seven miles more than A does in nine hours; How many miles does each walk per hour ?

13. In eleven hours C walks 12{1}{3} miles less than D does in twelve hours; and in five hours D walks 3{1}{4} miles less than C does in seven hours. How many miles does each walk per hour?

14. Find a fraction such that if 1 be added to its denominator it reduces to {1}{2}, and reduces to {3}{5} on adding 2 to its numerator.

15. Find a fraction which becomes {1}{2} on subtracting 1 from the numerator and adding 2 to the denominator, and reduces to {1}{3} on subtracting 7 from the numerator and 2 from the denominator.

16. If 1 be added to the numerator of a fraction it reduces to {1}{3}; if 1 be taken from the denominator it reduces to {1}{7}. Required the fraction.

17. If 2 be added to the numerator of a certain fraction the fraction will be increased by {1}{21}, and if be taken from its denominator the fraction becomes {2}{9}: find it.

18. The sum of a number of two digits and of the number formed by reversing the digits is 110, and the difference of the digits is 6: find the numbers.

19. The sum of the digits of a number is 13, and the difference between the number and that formed by reversing the digits is 27: find the numbers.

20. A certain number of two digits is three times the sum of its digits, and if 45 be added to it the digits will be reversed : find the number.

21. A certain number between 10 and 100 is eight times the sum of its digits, and if 45 be subtracted from it the digits will be reversed: find the number.

22. A man has a number of silver dollars and dines, and he observes that if the dollars were turned into dimes and the dimes into dollars he would gain $2.70 ; but if the dollars were turned into half-dollars and the dimes into quarters he would lose $ 1.30. How many of each had he ?

23. In a bag containing black and white balls, half the number of white is equal to a third of the number of black; and twice the whole number of balls exceeds three times the number of black balls by four. How many balls did the bag contain?