Solve the following questions on ratio – 1)  In one– day cricket match , Z conceded 27 runs in 9 overs & 2 balls , while H conceded  31 runs in 10 overs . Who had a better  performance ? 2) The ratio of the sums of money in three bags  A , B and C is 4 : 3 : 2 . If $ 50 is added to each of the bags , the ratio becomes 14 : 13 : 12 . Find the original sum of money in each of the bags .

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The ratio of sums of money in three bags A,B, and C is 4:3:2. If $50 is added to each of the bags, the ratio becomes 14:13:12.

Since the ratio of money in the bags was 4:3:2, there is some constant k such that the amount in bag A is 4k, the amount in B is 3k, and the amount in C is 2k.

Adding 50 to each bag we get the following equivalent ratios (a proportion):

4k+50:3k+50:2k+50=14:13:12

Then `(4k+50)/(2k+50)=14/12` (choose a corresponding pair of ratios to set equal):

`(2k+25)/(k+25)=7/6`

`12k+150=7k+175`

`5k=25`

`k=5`

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The original amounts in bags A,B, and C were $20,$15, $10.

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Check: 20:15:10= 4:3:2

70:65:60=14:13:12 as required.

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