We will learn how to divide a quantity in a given ratio and its application in the word problems on ratio.
1. John weights 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight.
Solution:
Let the previous weight be 5x.
5x = 65.7
x = \(\frac{65.7}{5}\)
x = 13.14
Therefore, the reduce weight = 4 × 13.14 = 52.56 kg.
2. Robin leaves $ 1245500 behind. According to his wish, the money is to be divided between his son and daughter in the ratio 3 : 2. Find the sum received by his son.
Solution:
We know if a quantity x is divided in the ratio a : b then the two parts are \(\frac{ax}{a + b}\) and \(\frac{bx}{a + b}\).
Therefore, the sum received by his son = \(\frac{3}{3 + 2}\) × $ 1245500
= \(\frac{3}{5}\) × $ 1245500
= 3 × $ 249100
= $ 747300
3. Two numbers are in the ratio 3 : 2. If 2 is added to the first and 6 is added to the second number, they are in the ratio 4 : 5. Find the numbers.
Solution:
Let the numbers be 3x and 2x.
According to the problem,
\(\frac{3x + 2}{2x + 6}\) = \(\frac{4}{5}\)
⟹ 5(3x + 2) = 4
⟹ 15x + 10 = 8x + 24
⟹ 15x – 8x = 24  10
⟹ 7x = 14
⟹ x = \(\frac{14}{7}\)
⟹ x = 2
Therefore, the original numbers are: 3x = 3 × 2 = 6 and 2x = 2 × 2 = 4.
Thus, the numbers are 6 and 4.
4. If a quantity is divided in the ratio 5 : 7, the larger part is 84. Find the quantity.
Solution:
Let the quantity be x.
Then the two parts will be \(\frac{5x}{5 + 7}\) and \(\frac{7x}{5 + 7}\).
Hence, the larger part is 84, we get
\(\frac{7x}{5 + 7}\) = 84
⟹ \(\frac{7x}{12}\) = 84
⟹ 7x = 84 × 12
⟹ 7x = 1008
⟹ x = \(\frac{1008}{7}\)
⟹ x = 144
Therefore, the quantity is 144.
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