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In a colony, 35% of the houses have a solar panel. There are 78 more houses without a panel than with one. How many houses are in the colony?

Class 7Comparing QuantitiesComparing Quantities
  • A260
  • B223
  • C120
  • D156

Step-by-Step Solution

Houses without a panel = 100% − 35% = 65%. The difference between the two groups is 65% − 35% = 30% of the colony, and that difference is 78 houses. So 30% of , giving . Check: 35% of 260 = 91, 65% of 260 = 169, and 169 − 91 = 78. The trap is matching 78 to 35% (which gives about 223) or to 65% (which gives 120) — the 78 belongs to the DIFFERENCE, not to either group.
Answer: A) 260

Key idea: Three forms of the same number

Fractions, decimals, and percentages are three notations for the same idea. Convert freely:

- **Fraction → percentage**: multiply by 100. .
- **Percentage → fraction**: divide by 100 and simplify. .
- **Decimal → percentage**: shift two places right. 0.34 = 34%.
- **Percentage → decimal**: shift two places left. 8% = 0.08.

With practice, this becomes automatic and you can move between forms without thinking.

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