 # Question

hi! can help us with this qn part (b)? tq!

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The ratio of the number of balls in Box A to the number of balls in Box B was 5:6 at first. 2/5 of the balls in Box A and 5/18 of the balls in Box B were red. The rest of the balls were yellow.

(a) What was the ratio of the number of yellow balls in Box A to the number of red balls in Box B at first?

(b) Ali took out a total of 50 balls from both boxes. He then put them back into Box A and Box B such that the number of red balls in each box became the same. The number of yellow balls in each box also became the same. In the end, how many yellow balls were there in each box?

 Box A Box B Total Total Balls 15u 18u 33u Red Balls 2/5 × 15u = 6u 5/18 × 18u = 5u 11u Yellow Balls 15u – 6u = 9u 18u – 5u = 13u 22u In the end Red Balls 5.5u 5.5u 11u Yellow Balls 11u 11u 22u

(a)

Ratio of Yellow Balls (A) to Red Balls (B) -> 9 : 5

(b)

Ali took (6u – 5.5u) = 0.5u red balls from A to put into B

He took (13u – 11u) = 2u yellow balls from B to put into A

2.5u = 50

1u = 20

11u = 220

Each box had 220 yellow balls in the end

(a)
5 : 6
15 : 18
(2/5) x 15 = 6
15 – 6 = 9
At first —
Box A : 15 units
red : 6 units
yellow : 9 units
Box B : 18 units
red : 5 units
yellow : 18 – 5 = 13 units
yellow balls in Box A : red balls in Box B is 9 : 5

(b)
red : 6 + 5 = 11 units
11/2 = 5.5
6 – 5.5 = 0.5
yellow : 9 + 13 = 22 units
22/2 = 11
13 – 11 = 2
2 + 0.5 = 2.5
2.5 units = 50
1 unit = 20
22/2 = 11
11 units = 11 x 20 = 220

Ans : (a) 9 : 5; (b) 220 yellow balls.