Question

Write (T) for true and (F) for false in case of each of the following:
(i) 51 : 68 : : 85 : 102
(ii) 36 : 45 : : 80 : 100
(iii) 30 bags : 18 bags : : Rs 450 : Rs 270
(iv) 81 kg : 45 kg : : 18 men : 10 men
(v) 45 km : 60 km : : 12 h : 15 h
(vi) 32 kg : Rs 36 : : 8 kg : Rs 9

Answer 1

(i) 51:68::85:102
Product of means = 68 × 85 = 5780
Product of extremes = 51 × 102 = 5202
Product of means ≠ Product of extremes
Hence, (F).
(ii) 36:45::80:100
Product of means = 45 ​× 80 = 3600
Product of extremes = 36 × 100 = 3600
Product of means = Product of extremes
Hence, (T).
(iii) 30 bags:18 bags::Rs 450:Rs 270
or 30:18::450:270
Product of means = 18 × 450 = 8100
Product of extremes = 30 ​× 270 = 8100
Product of means = Product of extremes
Hence, (T).
(iv) 81 kg:45 kg::18 men:10 men
or 81:45::18:10
Product of means = 45 × 18 = 810
Product of extremes = 81 × 10 = 810
Product of means = Product of extremes
Hence, (T).
(v) 45 km:60 km::12 h:15 h
or,45:60::12:15
Product of means = 60 × 12 = 720
Product of extremes = 45 × 15 = 675
Product of means ≠ Product of extremes
Hence, (F).
(vi) 32 kg:Rs 36::8 kg:Rs 9
Product of means = 36 × 8 = 288
Product of extremes = 32 × 9 = 288
Product of means = Product of extremes
Hence, (T).