Question

The sum of two numbers is 2490.if 6.5%of one number is equal to 8.5% of the other .then the numbers are

Answer 1

$Let\ the\ number\ be\ x\ and\ 2490-x. \\ \\ 6.5\% \ of\ one\ number = \frac {6.5}{100}x \times = \frac{13x}{200} \\ \\ 8.5\%\ of\ other\ number= \frac{8.5}{100} \big(2490 - x \big) \\ \\= \frac{17}{200} \big(2490-x \big) \\ \\ From\ the\ given\ condition,$$\\ \\ \frac{13x}{200} = \frac {17 \big(2490-x \big)}{200} \\ \\ \implies 13x + 17x = 42330 \\ \\ \implies x= \frac{42330}{30} = \fbox{1411 }\\ \\ \therefore Second\ number = 2490 - 1411 = \fbox {1079\ answer}$

Answer 2

Answer:

The numbers are 1079 and 1411

Step-by-step explanation:

Let 'x' and 'y' be the numbers

Then given,

the sum of the numbers   = 2490

x+y = 2490 -----------(1)

Also given,

6.5%of one number is equal to 8.5% of the other

6.5% ×x =  8.5% ×y

$\frac{6.5}{100} x$ = $\frac{8.5}{100} y$

6.5x = 8.5y

x = $\frac{8.5}{6.5} y$ = $\frac{17}{13}y$

x = $\frac{17}{13} y$ -------------(2)

Substitute the value of 'x' in equation (1) we get

$\frac{17}{13} y$ + y = 2490

$\frac{17y+13y}{13}$ = 2490

30y = 2490 × 13

y = $\frac{2490X 13}{30}$

y = 1079

x =   $\frac{17}{13}X 1079$ = 1411

∴The numbers are 1079 and 1411

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