1. The problem asks for the ratio of the amount Mr Sharma pays to the painter, simplified to its lowest terms.
2. Given the ratio of payments: painter : plumber : electrician = 245 : 252 : 224.
3. To simplify the ratio for the painter's amount, we find the greatest common divisor (GCD) of the three numbers 245, 252, and 224.
4. Calculate GCD:
- Prime factors of 245 = 5 \times 7^2
- Prime factors of 252 = 2^2 \times 3^2 \times 7
- Prime factors of 224 = 2^5 \times 7
5. The common prime factor is 7.
6. Divide each term by 7:
- Painter: $\frac{245}{7} = 35$
- Plumber: $\frac{252}{7} = 36$
- Electrician: $\frac{224}{7} = 32$
7. The simplified ratio is 35 : 36 : 32.
8. The question specifically asks for the ratio of the amount Mr Sharma pays to the painter, which is the first term, so the ratio is $35$ in lowest terms.
Final answer: The ratio of the amount Mr Sharma pays to the painter is $35$ (or simply the painter's share in the simplified ratio is 35).
Payment Ratio D25Cae
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.