Neco 2019 Economics Question 33

An economy's Human Development Index (HDI) is the arithmetic mean of three equally weighted indices: health (H), education (E) and income (I). Currently the overall HDI is 0.720, with H = 0.800 and E = 0.650. The income index I is therefore unknown. The government aims to raise the HDI to at least 0.770 within 5 years. Health and education indices can each improve by at most 0.010 per year, while the income index can improve by at most 0.015 per year. Assuming health and education improve at their maximum rates, determine the minimum constant annual increase required for the income index to achieve the target HDI, and give the required income index value after 5 years.