Q.If any population has equal birth-rate and death-rate then its age pyramid X, vital index Y and population is Z

An age (population) pyramid whose Pre-Reproductive and Reproductive bands are both broad — the outline bulging outward at the Reproductive tier rather than tapering steadily like a true triangle — and narrows only at the Post-Reproductive top, represents a Stable population, where birth rate and death rate are roughly equal.

Figure: A human age-structure pyramid built from stacked horizontal bars, divided into three zones from bottom to top: 'Pre-Reproductive' (widest, at the base), 'Reproductive' (middle band), and 'Post-Reproductive' (narrowest, at the top) — the silhouette bulges out at the Reproductive band and narrows above and below it.

Age pyramids represent the age distribution of pre-reproductive, reproductive and post-reproductive individuals in a population, and their overall shape indicates whether the population is growing, stable, or declining:

• Expanding population: a true triangular/pyramidal shape, with each band narrower than the one below it in a steady taper — a large Pre-Reproductive base, a smaller Reproductive band, and the smallest Post-Reproductive band — reflecting a high birth rate and a young, rapidly growing population.
• Stable population: a broad, bell/urn-like outline where the Pre-Reproductive and Reproductive tiers are of comparable, large width (the silhouette bulges rather than tapering sharply), and only the Post-Reproductive band narrows — reflecting roughly equal birth and death rates, so the population size stays fairly constant. …

A pyramid with the largest pre-reproductive class (broad base tapering upward) indicates an EXPANDING (growing) population.

Age pyramids show the proportion of individuals in pre-reproductive, reproductive and post-reproductive age groups:

• Here the percentages are in decreasing order: pre-reproductive > reproductive > post-reproductive. This gives a broad-based, triangular pyramid. …

An age pyramid whose base (pre-reproductive) is narrower than its bulging middle (reproductive) segment, with an even narrower top (post-reproductive), depicts a declining population.

Age pyramids show the proportion of pre-reproductive, reproductive and post-reproductive individuals in a population, and their overall shape tells us whether the population is growing, stable, or shrinking:

• Expanding population: broad-based, triangular pyramid - pre-reproductive (base) is the widest group, since a high birth rate keeps adding many young individuals.
• Stable population: pre-reproductive and reproductive groups are of roughly comparable width. …

A narrow-based, urn-shaped age pyramid signals a declining population, because it shows fewer young individuals than older ones.

Age pyramids illustrate a population's age structure and, by their shape, indicate its growth trend. An urn-shaped age pyramid, which is narrow at the base (representing the pre-reproductive/young age class) and relatively broader in the middle/upper (older) age classes, indicates a declining population — because the number of young individuals being added to the population is smaller than the number of individuals in the older age classes, meaning the population' …