IPMAT 2025 Exam Solved Papers

$$7 m+11 n=200$$It is given that both m and n are positive integers. We need to find one integer pair of $(m, n)$ that satisfy the equation for these questions.If we put the value of $\mathrm{n}=1$, then the value of $\mathrm{m}=27$. Thus, one solution will be (27,1).Now, to find the next solution of n, we need to add the coefficient of m in the original value of n, and to find the next value of m, we need to subtract the coefficient of n in the original value of m. (One should be added, the other should be subtracted. Since we need the positive values of m and n, thus we are adding in n, and subtracting from m). We will continue this process till we get any value of m or n as negative.Thus, the other solutions of these equations will be - $(\mathrm{m}, \mathrm{n})=(16,8),(5,15)$If $(m, n)=(27,1) \Rightarrow m+n=28$.If $(\mathrm{m}, \mathrm{n})=(16,8) \Rightarrow \mathrm{m}+\mathrm{n}=24$.If $(\mathrm{m}, \mathrm{n})=(5,15) \Rightarrow \mathrm{m}+\mathrm{n}=20$.Thus, the minimum value of $\mathrm{m}+\mathrm{n}=20$.