The soldiers in two armies when they met in a battle were in the ratio of 10 : 3. Their respective losses were as 20 : 3 and the survivors as 40 : 13. If the number of survivors in the larger army be 24,000, find the original number of soldiers in each army ?
Question
The soldiers in two armies when they met in a battle were in the ratio of 10 : 3. Their respective losses were as 20 : 3 and the survivors as 40 : 13. If the number of survivors in the larger army be 24,000, find the original number of soldiers in each army ?
Solution
Step 1: Understand the given ratios
The ratio of soldiers in the two armies is given as 10:3. This means that for every 10 soldiers in the larger army, there are 3 soldiers in the smaller army.
The ratio of survivors in the two armies is given as 40:13. This means that for every 40 survivors in the larger army, there are 13 survivors in the smaller army.
Step 2: Use the given information to form an equation
We know that the number of survivors in the larger army is 24,000. According to the ratio of survivors, this means that the number of survivors in the smaller army is (13/40)*24,000 = 7,800.
Step 3: Calculate the original number of soldiers in each army
The ratio of the original number of soldiers in the two armies is 10:3. So, the original number of soldiers in the larger army is (10/3)7,800 = 26,000 and the original number of soldiers in the smaller army is 37,800 = 23,400.
So, the original number of soldiers in the larger army was 26,000 and in the smaller army was 23,400.
Similar Questions
When a new group of 45 boys joined a concert, the ratio of the number of boys to the number of girls present became 2 : 3. The initial ratio was 5 : 9. How many more girls than boys were there in the end?
An army of 12000 consists of Europeans and Indians. The average height of a European is 5 ft 10 inches and that of an Indian 5 ft 9 inches and that of the whole army is 5 ft 9 3/4 inches. Find the numbers of Indians in the army?
In a school the total number of students was 350 and the ratio of the number of boys and girls was 4: 3. After a few days 30 girls joined the school but a few boys left, as a result the ratio of the boys and the girls became 5: 6. Find the number of boys who left the school.35402550
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
The ratio of the number of boys and girls in a school is 5:9 and the total number of students is 224. If 64 girls left the school and some boys joined the ratio becomes 6 : 5. Find the number boys who joined.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.