Problem Setup
Let the first number be represented by the variable $x$. The problem provides relationships between three numbers based on percentages.
Number Relationships
- The second number is 150% of the first number.
- The third number is 80% of the second number.
Calculating the Third Number
First, express the second number in terms of $x$:
Second number = $150\% \times x = \frac{150}{100} \times x = 1.5x$
Next, calculate the third number using the value of the second number:
Third number = $80\% \times (\text{Second number})$
Third number = $80\% \times (1.5x)$
Third number = $\frac{80}{100} \times 1.5x$
Third number = $0.8 \times 1.5x$
Third number = $1.2x$
Finding the Ratio
The question asks for the ratio of the first number to the third number.
Ratio = $\frac{\text{First number}}{\text{Third number}}$
Ratio = $\frac{x}{1.2x}$
Simplify the ratio:
Ratio = $\frac{1}{1.2}$
To express this as a ratio of integers, convert the decimal to a fraction: $1.2 = \frac{12}{10} = \frac{6}{5}$.
Ratio = $\frac{1}{\frac{6}{5}}$
Ratio = $1 \times \frac{5}{6}$
Ratio = $\frac{5}{6}$
Therefore, the ratio of the first to the third number is 5:6.
Similar Questions
If \((x+y):(x-y)=5:2\), find \((x^3+y^3):(x^3-y^3)\)
What should be subtracted from 7, 9, 8, 11 so that the remaining numbers may be proportional?
- A ribbon is cut into three pieces in the ratio 2:3:5. If the length of the longest piece is 20 cm, what is the total length of the ribbon?
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The monthly incomes of A, B and C are in the ratio 2:9:3 and their expenses are in the ratio 3:9:5. If A’s saving is half of his total income, then savings of A, B and C are, respectively, in the ratio of:
If 20% of (P + Q) = 50% of (P – Q), then find the ratio P : Q.
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
