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.
● Ratio and proportion
From Word Problems on Ratio to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 18, 24 02:58 AM
Apr 18, 24 02:15 AM
Apr 18, 24 01:36 AM
Apr 18, 24 12:31 AM
Apr 17, 24 01:32 PM