Question

10 years ago the ages of a and b were in the ration of 13:17, 17 years from now the ratio of their ages wil be 10:11, what is the age of B at present

Answer 1

Answer:age of B is 10 years

Step-by-step explanation:

As the ratio becomes 10:11 after 17 years A's age is a multiple of 10 after adding 17 to it.

but it is currently a multiple of 13.

similarly the current age of B is a multiple of 17 and would be a multiple of 11 after 17 years.

13×1=13

13×2=26

13×3=39

13×4=52

13×5=65

13×6=78

13×7=91

13×8=104

13×9=117

13×10=130

adding 17 to each number we get

13+17=30

26+17=43

39+17=56

52+17=69

65+17=82

78+17=95

91+17=108

104+17=121

117+17=134

130+17=147

as only 13×1+17 gives a multiple of 10 age of A is 1 year

similarly calculate age of B

17×1=17

17×2=34

17×3=52

17×4=68

17×5=85

17×6=102

17×7=119

17×8=136

17×9=153

17×10=170

adding 17 to each number we get

17+17=34

34+17=52

52+17=68

68+17=85

85+17=102

102+17=119

119+17=136

136+17=153

153+17=170

170+17=187

as 17×10+17 gives a multiple of 11,age of B is 10 years

Answer 2

Answer:

The present age of a is 23 years and present age of b is 27 years

Step-by-step explanation:

Let the present age of a be $x$ years

Let the present age of b be $y$ years

10 years ago,

Age of a $=x - 10$ years

Age of b $= y - 10$ years

Given that ratio of age of a and b 10 years ago is 13 : 17

Thus, we have

$\frac{x - 10}{y - 10} = \frac{13}{17}\\\\ 17(\,x - 10)\, = 13(\,y - 10)\,\\\\ 17x - 170 = 13y - 130 \\\\ 17x - 13y = - 130 + 170\\\\ 17x - 13y = 40 ----- (1)$

17 years after,

Age of a $=x + 17$ years

Age of b $= y + 17$ years

Given that ratio of age of a and b 17 years after is 10 : 11

Thus, we have

$\frac{x + 17}{y + 17} = \frac{10}{11}\\\\ 11(\,x + 17)\, = 10(\,y + 17)\,\\\\ 11x + 187 = 10y + 170 \\\\ 11x - 10y = 170 - 187\\\\ 11x - 10y = -17 ----- (2)$

Solving (1) and (2), we get

 17x - 13y = 40 ----× 11

 11x - 10y = -17 -----× 17

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 187x - 143y = 440

 187x - 170y = -289

(-)       (+)          (+)

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       27y = 729

         y = $\frac{729}{27}$

         y = 27 years

Putting value of v in (1), we get

$17x - 13(\, 27)\, = 40\\\\ 17x - 351 = 40\\\\ 17x = 391 \\\\ x = \frac{391}{17}\\\\ x = 23\hspace{0.1cm}years$

Thus, present age of a is 23 years and present age of b is 27 years