aman has a tractor.the sum of the radii of two wheels of tractor is 98cm.and the diffrence of their circumference is 176cm.find the diameter of wheels.

Suppose $r_1 \mathrm{and} r_2$ be the radius of wheels of tractor.
Circumference of the wheel of radius $r_1$ = $2{\mathrm{\pi r}}_1$
And the circumference of the wheel of radius $r_2$ = $2{\mathrm{\pi r}}_2$
Now, according to the question, sum of radii of two wheels is 98 cm, so we have;
$r_1+r_2 = 98$....  (i)
And the difference of their circumference is 176 cm, so we have;
$$\begin{gathered} 2{\mathrm{\pi r}}_1-2{\mathrm{\pi r}}_2 = 176 \\ \Rightarrow 2\mathrm{\pi }\left({\mathrm{r}}_1-{\mathrm{r}}_2\right) = 176 \\ \Rightarrow 2\times \frac{22}{7}\left({\mathrm{r}}_1-{\mathrm{r}}_2\right) = 176 \\ \Rightarrow {\mathrm{r}}_1-{\mathrm{r}}_2 = 176\times \frac{7}{22}\times \frac{1}{2} \\ \Rightarrow {\mathrm{r}}_1-{\mathrm{r}}_2 =28 ........ \left(\mathrm{ii}\right) \end{gathered}$$
Solving (i) and (ii) we get;
$$\begin{gathered} r_1+r_2+r_1-r_2 = 98+28 \\ \Rightarrow 2r_1 = 126 \\ \Rightarrow r_1 = \frac{126}{2} = 63 \end{gathered}$$
Therefore, the diameter of wheels are 28 $\times$ 2 i.e. 56 cm and 63 $\times$ 2 i.e.126 cm