We divided the line AB into two parts in a ratio of 3: 5. The longer part was 6 cm longer than the shorter part. How long in cm was the whole line?  Did you find an error or inaccuracy? Feel free to write us. Thank you! Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it.
Rules of dividing a quantity in three given ratios is explained below along with the different types of examples. If a quantity K is divided into three parts in the ratio X : Y : Z, then First part = X/(X + Y + Z) × K, Second part = Y/(X + Y + Z) × K, Third part = Z/(X + Y + Z) × K. For example, suppose, we have to divide $ 1200 among X, Y, Z in the ratio 2 : 3 : 7. This means that if X gets 2 portions, then Y will get 3 portions and Z will get 7 portions. Thus, total portions = 2 + 3 + 7 = 12. So, we have to divide $ 1200 into 12 portions and then distribute the portions among X, Y, Z according to their share. Thus, X will get 2/12 of $ 1200, i.e., 2/12 × 1200 = $ 200 Y will get 3/12 of $ 1200, i.e., 3/12 × 1200 = $ 300 Z will get 7/12 of $ 1200, i.e., 7/12 × 1200 = $ 700 Solved examples: 1. If $ 135 is divided among three boys in the ratio 2 : 3 : 4, find the share of each boy. Solution: The sum of the terms of the ratio = 2 + 3 + 4 = 9 Share of first boy = 2/9 × 135 = $ 30. Share of second boy = 3/9 × 315 = $ 45. Share of first boy = 4/9 × 315 = $ 60. Thus, the required shares are $ 30, $ 45 and $ 60 respectively. 2. Divide 99 into three parts in the ratio 2 : 4 : 5. Solution: Since, 2 + 4 + 5 = 11. Therefore, first part = 2/11 × 99 = 18. Second part = 4/11 × 99 = 36. And, third part = 5/11 × 99 = 45. 3. 420 articles are divided among A, B and C, such that A gets three-times of B and B gets five-times of C. Find the number of articles received by B. Solution: Let the number of articles C gets = 1 The number of article that B gets = five times of C = 5 × 1 = 5. And, the number of articles that A gets = three times of B = 3 × 5 = 15. Therefore, A : B : C = 15 : 5 : 1 And, A + B + C = 15 + 5 + 1 = 21 The number of articles received by B = 5/21 × 420 = 100 The above examples on dividing a quantity in three given ratios will help us to solve different types of problems on ratios. 6th Grade Page From Dividing a Quantity in Three given Ratios to HOME PAGE
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We will follow the rules of dividing a quantity in a given ratio (two or three) to solve different types of problems. 1. 20 apples are distributed between Aaron and Ben in the ratio 2 : 3. Find, how many does each get? Solution: Aaron and Ben get apples in the ratio 2 : 3 i.e. if Aaron gets 2 parts, B should get 3 parts. In other words, if we make (2 + 3) = 5 equal parts, then Aaron should get 2 parts out of these 5 equal part i.e. Aaron gets = 2/5 of the total number of apples = 2/5 of 20 = 2/5 × 20 = 8 apples Similarly, Ben gets 3 parts out of 5 equal parts i.e. Ben gets = 3/5 of the total number of apples = 3/5 of 20 = 3/5 × 20 = 12 apples Therefore, Aaron gets 8 apples and Ben gets 12 apples. In other way we can solve this by the direct method, Since, the given ratio = 2 : 3 and 2 + 3 = 5 Therefore, Aaron gets = 2/5 of the total number of apples = 2/5 × 20 apples = 8 apples and, Ben gets = 3/5 of the total number of apples = 3/5 × 20 apples = 12 apples 2. Divide $ 120 between David and Jack in the ratio 3 : 5. Solution: Ratio of David’s share to Jack’s share = 3 : 5 Sum of the ratio terms = 3 + 5 = 8 Thus we can say David gets 3 parts and Jack gets 5 parts out of every 8 parts. Therefore, David’s share = $(3 × 120)/8 = $45 And, Jack’s share = $(5 × 120)/8 = $75 Therefore, David get $45 and Jack gets $75 More solved problems on dividing a quantity in a given ratio: 3. Divide $260 among A, B and C in the ratio 1/2 : 1/3 : 1/4. Solution: First of all convert the given ratio into its simple form. Since, L.C.M. of denominators 2, 3 and 4 is 12. Therefore, 1/2 : 1/3 : 1/4 = 1/2 × 12 : 1/3 × 12 : 1/4 × 12 = 6 : 4 : 3 And, 6 + 4 + 3 = 13 Therefore, A’ share = 6/13 of $260 = $6/13 × 260 = $120 B’ share = 4/13 of $260 = $4/13 × 260 = $80 C’ share = 3/13 of $260 = $3/13 × 260 = $60 Therefore, A get $120, B gets $80 and C gets $60 4. Two numbers are in the ratio 10 : 13. If the difference between the numbers is 48, find the numbers. Solution: Let the two numbers be 10 and 13 Therefore, the difference between these numbers = 13 – 10 = 3 Now applying unitary method we get, When difference between the numbers = 3; 1st number = 10 ⇒ when difference between the numbers = 1; 1st number = 10/3 ⇒ when difference between the numbers = 48; 1st number = 10/3 × 48 = 160 Similarly, in the same way we get; When difference between the numbers = 3; 1st number = 13 ⇒ when difference between the numbers = 1; 1st number = 13/3 ⇒ when difference between the numbers = 48; 1st number = 13/3 × 48 = 208 Therefore, the required numbers are 160 and 208. The above examples on dividing a quantity in a given ratio will give us the idea to solve different types of problems on ratios. 6th Grade Page From Dividing a Quantity in a given Ratio to HOME PAGE
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If 90 is divided into two parts in the ratio of 2 : 3 what is the difference between these two parts
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