Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is
Question:
Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is
Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is
Options
Answer: 7:9
Explanation:
Step 1: Let Rajesh’s land have wheat = x, mustard = 20 − x Vimal’s land: wheat : mustard = 5 : 3 → total 30 hectares Sum of parts = 5 + 3 = 8 Each part = 30 / 8 = 3.75 hectares Vimal’s wheat = 5 × 3.75 = 18.75 Vimal’s mustard = 3 × 3.75 = 11.25 Step 2: Total wheat and mustard Total wheat = x + 18.75 Total mustard = (20 − x) + 11.25 = 31.25 − x Given total wheat : mustard = 11 : 9 (x + 18.75) / (31.25 − x) = 11 / 9 Step 3: Solve for x 9(x + 18.75) = 11(31.25 − x) 9x + 168.75 = 343.75 − 11x 20x = 175 → x = 8.75 Rajesh’s wheat = 8.75 Rajesh’s mustard = 20 − 8.75 = 11.25 Step 4: Ratio on Rajesh’s land Wheat : mustard = 8.75 : 11.25 = 7 : 9
Explanation:
Step 1: Let Rajesh’s land have wheat = x, mustard = 20 − x Vimal’s land: wheat : mustard = 5 : 3 → total 30 hectares Sum of parts = 5 + 3 = 8 Each part = 30 / 8 = 3.75 hectares Vimal’s wheat = 5 × 3.75 = 18.75 Vimal’s mustard = 3 × 3.75 = 11.25 Step 2: Total wheat and mustard Total wheat = x + 18.75 Total mustard = (20 − x) + 11.25 = 31.25 − x Given total wheat : mustard = 11 : 9 (x + 18.75) / (31.25 − x) = 11 / 9 Step 3: Solve for x 9(x + 18.75) = 11(31.25 − x) 9x + 168.75 = 343.75 − 11x 20x = 175 → x = 8.75 Rajesh’s wheat = 8.75 Rajesh’s mustard = 20 − 8.75 = 11.25 Step 4: Ratio on Rajesh’s land Wheat : mustard = 8.75 : 11.25 = 7 : 9
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