Final answer:
By setting up an equation based on the initial and new ratios of bungalows to flats, and solving for 'x,' we determine that there are now 77 bungalows and 55 flats in the village.
Step-by-step explanation:
The question involves solving a problem with ratios and algebra to find out how many bungalows and flats there are in a village now, given a change in ratio after the construction of additional housing units.
Initially, the ratio of bungalows to flats was 3:2. After building 11 more bungalows and 11 more flats, the new ratio became 7:5.
Let's denote the original number of bungalows as 3x and the original number of flats as 2x.
After construction, the number of bungalows became 3x + 11 and the number of flats became 2x + 11. The new ratio is therefore:
(3x + 11) : (2x + 11) = 7 : 5
To solve for x, we can set up a proportion:
(3x + 11) / (2x + 11) = 7 / 5
Cross-multiplying gives us:
5(3x + 11) = 7(2x + 11)
15x + 55 = 14x + 77
Solving for x gives us x = 22. So the original number of bungalows was 3x = 66 and the original number of flats was
2x = 44. With 11 new buildings of each type, the village now has 66 + 11 = 77 bungalows and 44 + 11 = 55 flats.