A vegetable seller sells tomato, brinjal and cauliflower in the ratio 1 3 : 2 5 : 3 4 . If their total weight is 178 kg , then find the weight of the cauliflower.

Given. Total weight of vegetables = 178 kg We have to find the weight of cauliflower. Ratio of weights of tomato, brinjal and cauliflower = 1 3 : 2 5 : 3 4 L.C.M of denominators 3 , 5 and 4 is 60 . 1 3 × 20 20 = 20 60 ; 2 5 × 12 12 = 24 60 ; 3 4 × 15 15 = 45 60 So, ratio = 20 : 24 : 45 Weight of cauliflower = 45 20 + 24 + 45 × 178 = 45 × 2 = 90 kg Hence, the weight of cauliflower is 90 kg .

There are three numbers which are in the ratio 3 : 4 7 : 2 5 . If the sum of the numbers is 278 , then find the three numbers.

Let the numbers be 3 x , 4 x 7 , 2 x 5 . Sum of the numbers = 278 Therefore, 3 x + 4 x 7 + 2 x 5 = 278 105 x + 20 x + 14 x 35 = 278 139 x = 278 × 35 x = 278 × 35 139 x = 9730 139 = 70 So, 3 x = 3 × 70 = 210 4 x 7 = 4 × 70 7 = 40 2 x 5 = 2 × 70 5 = 28 Hence, the three numbers are 210 , 40 , 28 respectively.