Figure It Out: Sharing & Mixtures

Figure It Out (Page 175)

1. Divide ₹4,500 in ratio 2:3

• Total parts = 5. One part = $4500/5 = 900$.
• Part 1: $2 \times 900 = 1800$.
• Part 2: $3 \times 900 = 2700$.

2. Acid and Water (1:5)

• Total parts = 6. Total vol = 240 mL.
• One part = $240/6 = 40$ mL.
• Acid = $1 \times 40 = 40$ mL.
• Water = $5 \times 40 = 200$ mL.

3. Paint Mixture (3:5)

• Total 40 mL. Ratio 3:5.
• Blue = $\frac{3}{8} \times 40 = 15$ mL.
• Yellow = $\frac{5}{8} \times 40 = 25$ mL.
• Adding 20 mL Yellow:
  • New Yellow = $25 + 20 = 45$ mL.
  • Blue stays 15 mL.
  • New Ratio = $15 : 45 = 1 : 3$.

4. Idli Mixture (2:1)

• Total 6 cups. Ratio 2:1.
• Rice = $\frac{2}{3} \times 6 = 4$ cups.
• Urad Dal = $\frac{1}{3} \times 6 = 2$ cups.

5. Paint Buckets

• Bucket 1: Ratio 3:5 (Red:Yellow). Let volume be $V$.
  • Red = $\frac{3}{8}V$, Yellow = $\frac{5}{8}V$.
• Bucket 2: Pure Yellow. Volume $V$ (assuming same size bucket).
  • Red = 0, Yellow = $V$.
• Total Mixture:
  • Total Red = $\frac{3}{8}V$.
  • Total Yellow = $\frac{5}{8}V + V = \frac{13}{8}V$.
• New Ratio: $\frac{3}{8}V : \frac{13}{8}V \rightarrow 3 : 13$.