1. **Problem Statement:** We analyze the export data of Companies X, Y, and Z from 1993 to 1999 to answer several questions about their export changes. 2. **Given Data (in Rs. crores):** - Company Y: 1993=80, 1994=40, 1995=approx 60, 1996=approx 80, 1997=approx 100, 1998=approx 120, 1999=140 - Company X: 1993=30, 1994=approx 60, 1995=120, 1996=approx 110, 1997=100, 1998=50, 1999=120 - Company Z: 1993=60, 1994=approx 70, 1995=120, 1996=approx 90, 1997=approx 80, 1998=approx 85, 1999=90 3. **Formulas and Rules:** - Yearly increase = Export in current year - Export in previous year - Percentage increase = $\frac{\text{Increase}}{\text{Previous year export}} \times 100$ - For ratio, multiply exports by given percentage increase factors - To double exports, new export = 2 × reference export --- **(a) Steepest rise in exports compared to previous year:** Calculate yearly increases for each company: - Company Y: 1994: 40-80 = -40, 1995: 60-40=20, 1996: 80-60=20, 1997: 100-80=20, 1998: 120-100=20, 1999: 140-120=20 - Company X: 1994: 60-30=30, 1995: 120-60=60, 1996: 110-120=-10, 1997: 100-110=-10, 1998: 50-100=-50, 1999: 120-50=70 - Company Z: 1994: 70-60=10, 1995: 120-70=50, 1996: 90-120=-30, 1997: 80-90=-10, 1998: 85-80=5, 1999: 90-85=5 The steepest rise is Company X in 1999 with an increase of 70 crores. --- **(b) Highest percentage increase in 1999 compared to 1993:** Calculate percentage increase: - Company Y: $\frac{140-80}{80} \times 100 = 75\%$ - Company X: $\frac{120-30}{30} \times 100 = 300\%$ - Company Z: $\frac{90-60}{60} \times 100 = 50\%$ Highest percentage increase is Company X with 300%. --- **(c) Exports in 2000 with given increases:** - Company X: $120 \times 1.10 = 132$ - Company Y: $140 \times 1.20 = 168$ - Company Z: $90 \times 1.30 = 117$ Ratio of exports in 2000 = $132 : 168 : 117$ Simplify by dividing by 3: $44 : 56 : 39$ --- **(d) Percent increase needed in 1996 for X and Y to double Z's 1996 exports:** - Exports in 1996: - Company X = 110 - Company Y = 80 - Company Z = 90 - Double of Z's 1996 exports = $2 \times 90 = 180$ Let percent increase for X be $p_x$ and for Y be $p_y$. We want: $$110 \times \left(1 + \frac{p_x}{100}\right) = 180$$ $$80 \times \left(1 + \frac{p_y}{100}\right) = 180$$ Solve for $p_x$: $$1 + \frac{p_x}{100} = \frac{180}{110} = \frac{18}{11} \approx 1.6364$$ $$p_x = (1.6364 - 1) \times 100 = 63.64\%$$ Solve for $p_y$: $$1 + \frac{p_y}{100} = \frac{180}{80} = 2.25$$ $$p_y = (2.25 - 1) \times 100 = 125\%$$ --- **(e) Difference in exports in 1992 between Z and X:** - 1993 exports: - Z = 60 - X = 30 - 1992 exports: - Z = $60 \times (1 - 0.30) = 42$ - X = $30 \times (1 + 0.30) = 39$ Difference = $42 - 39 = 3$ crores --- **Final Answers:** (a) Company X in 1999 had the steepest rise of 70 crores. (b) Company X had the highest percentage increase of 300% in 1999 compared to 1993. (c) Ratio of exports in 2000 is $44 : 56 : 39$ for Companies X, Y, and Z respectively. (d) Company X needs a 63.64% increase and Company Y needs a 125% increase in 1996 to double Company Z's 1996 exports. (e) The difference between exports of Companies Z and X in 1992 is 3 crores.