A sum of ₹5,000 is divided between two people such that twice the first person's share exceeds the second person's share by ₹1,000. Using Cramer's Rule, find each person's share.

Question

Accepted Answer

**Setting up the equations**

Let $x$ = the first person's share and $y$ = the second person's share (both in rupees). The problem states:
$$x+y=5000$$
$$2x-y=1000 \quad(	ext{twice the first share EXCEEDS the second by ₹1,000})$$

**Forming $D$**

$$D=\begin{vmatrix}1&1\2&-1\end{vmatrix}=1(-1)-1(2)=-1-2=-3$$

Since $D
eq0$, a unique solution exists.

**Forming $D_x$**

$$D_x=\begin{vmatrix}5000&1\1000&-1\end{vmatrix}=5000(-1)-1(1000)=-5000-1000=-6000$$

**Forming $D_y$**

$$D_y=\begin{vmatrix}1&5000\2&1000\end{vmatrix}=1(1000)-5000(2)=1000-10000=-9000$$

**Solving**

$$x=\frac{-6000}{-3}=2000 \qquad y=\frac{-9000}{-3}=3000$$

So the first person receives ₹2,000 and the second person receives ₹3,000. …

Q.A sum of ₹5,000 is divided between two people such that twice the first person's share exceeds the second person's share by ₹1,000. Using Cramer's Rule, find each person's share.

Concept understanding — Cramer's Rule for Two Linear Equations in Two Unknowns

Q.A sum of ₹5,000 is divided between two people such that twice the first person's share exceeds the second person's share by ₹1,000. Using Cramer's Rule, find each person's share.

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