Numerical Problems on Measures of Fertility and Mortality
(Solved Examples for JKSSB & Statistics Exams 2026)
Prepared by Home Academy
These numerical problems are frequently asked in JKSSB, SSC, Statistics, and University exams. Students must clearly understand the formulas and calculation steps.
Important Formulas for Numerical Problems
| Measure | Formula |
|---|---|
| Crude Fertility Rate (CFR) | CFR = (Number of live births / Number of women aged 15–49) × 1000 |
| Age Specific Fertility Rate (ASFR) | ASFR = (Births in specific age group / Women in that age group) × 1000 |
| Gross Reproduction Rate (GRR) | GRR = Total Fertility Rate × proportion of female births |
| Net Reproduction Rate (NRR) | NRR = GRR × survival rate of females |
| Crude Death Rate (CDR) | CDR = (Total deaths / Mid-year population) × 1000 |
| Infant Mortality Rate (IMR) | IMR = (Infant deaths / Live births) × 1000 |
Problem 1: Crude Fertility Rate
In a town the number of live births during a year is 4200 and the number of women aged 15–49 years is 28,000.
Find the Crude Fertility Rate.
Solution
CFR = (Live births / Women aged 15–49) × 1000
CFR = (4200 / 28000) × 1000
CFR = 0.15 × 1000
CFR = 150
Answer
Crude Fertility Rate = 150 births per 1000 women
Problem 2: Age Specific Fertility Rate
The number of births to women aged 20–24 is 1500.
The number of women in this age group is 12,000.
Find ASFR.
Solution
ASFR = (Births in age group / Women in age group) × 1000
ASFR = (1500 / 12000) × 1000
ASFR = 0.125 × 1000
ASFR = 125
Answer
ASFR = 125 births per 1000 women
Problem 3: Crude Death Rate
In a city the total deaths during a year are 3500 and the mid-year population is 200,000.
Find Crude Death Rate.
Solution
CDR = (Total deaths / Mid-year population) × 1000
CDR = (3500 / 200000) × 1000
CDR = 0.0175 × 1000
CDR = 17.5
Answer
Crude Death Rate = 17.5 per 1000 population
Problem 4: Infant Mortality Rate
In a district there were 12,000 live births and 360 infant deaths (below 1 year).
Find IMR.
Solution
IMR = (Infant deaths / Live births) × 1000
IMR = (360 / 12000) × 1000
IMR = 0.03 × 1000
IMR = 30
Answer
Infant Mortality Rate = 30 per 1000 live births
Problem 5: Gross Reproduction Rate
Suppose Total Fertility Rate (TFR) = 2.8.
Proportion of female births = 0.488.
Find GRR.
Solution
GRR = TFR × proportion of female births
GRR = 2.8 × 0.488
GRR = 1.3664
Answer
Gross Reproduction Rate ≈ 1.37 daughters per woman
Problem 6: Net Reproduction Rate
If GRR = 1.37 and female survival rate to reproductive age = 0.80, find NRR.
Solution
NRR = GRR × survival rate
NRR = 1.37 × 0.80
NRR = 1.096
Answer
Net Reproduction Rate ≈ 1.10
Interpretation
Since NRR > 1, the population is increasing.
Problem 7: Age Specific Death Rate
In the age group 60–70 years, there were 400 deaths in a population of 8000 persons.
Find ASDR.
Solution
ASDR = (Deaths in age group / Population of that age group) × 1000
ASDR = (400 / 8000) × 1000
ASDR = 0.05 × 1000
ASDR = 50
Answer
Age Specific Death Rate = 50 per 1000 population
Problem 8 (JKSSB Pattern Table Question)
Calculate ASFR for the following data.
| Age Group | Births | Women |
|---|---|---|
| 15–19 | 200 | 5000 |
| 20–24 | 600 | 4000 |
| 25–29 | 500 | 3500 |
Solution
ASFR = (Births / Women) × 1000
15–19
ASFR = (200 / 5000) × 1000 = 40
20–24
ASFR = (600 / 4000) × 1000 = 150
25–29
ASFR = (500 / 3500) × 1000 = 142.86
Final Table
| Age Group | ASFR |
|---|---|
| 15–19 | 40 |
| 20–24 | 150 |
| 25–29 | 142.86 |
Most Important Tips for Numerical Exams
Fertility rates are usually expressed per 1000 women.
Mortality rates are expressed per 1000 population.
NRR > 1 → Population growth.
NRR = 1 → Stable population.
GRR ignores mortality but NRR includes mortality.
Most Expected Numerical MCQs (JKSSB 2026)
MCQ 1
If births = 3000 and women aged 15–49 = 20,000, the CFR is:
A. 120
B. 150
C. 160
D. 180
Answer: B
MCQ 2
If infant deaths = 200 and live births = 10,000, IMR is:
A. 10
B. 15
C. 20
D. 25
Answer: C
MCQ 3
NRR greater than 1 indicates:
A. Declining population
B. Stable population
C. Increasing population
D. Zero growth
Answer: C