Set 2: Ratio and Proportion (Medium)
1.
A basket contains apples, bananas, and oranges in the ratio 3 : 2 : 5. If there are 12 bananas, how many total pieces of fruit are there?
Solution (C):
Ratio is \(3x : 2x : 5x\).
Bananas = \(2x = 12 \implies x = 6\).
Total fruit = \(3x + 2x + 5x = 10x\).
Total = \(10(6) = 60\).
2.
In a bag, the ratio of green marbles to yellow marbles is 4:7. If there are 27 more yellow marbles than green marbles, how many green marbles are there?
Solution (B):
Let Green = \(4x\) and Yellow = \(7x\).
Difference: \(7x – 4x = 27 \implies 3x = 27 \implies x = 9\).
Green marbles = \(4x = 4(9) = 36\).
3.
A salary is increased by 20% to become $2400. What was the original salary?
Solution (D):
Let original salary be \(S\).
\(1.20 \times S = 2400\).
\(S = \frac{2400}{1.2} = 2000\).
4.
In a school, the ratio of boys to girls is 5:3. If there are 400 students in total, how many girls are there?
Solution (A):
Total ratio parts = \(5 + 3 = 8\).
One part = \(400 \div 8 = 50\).
Number of girls = \(3 \text{ parts} \times 50 = 150\).
5.
If the degree measures of the three angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?
Solution (C):
Sum of angles in a triangle = 180°.
Parts: \(2x + 3x + 4x = 9x\).
\(9x = 180 \implies x = 20\).
Largest angle = \(4x = 4(20) = 80^\circ\).
6.
A car dealership sells only sedans and SUVs in a ratio of 2:5. If they have 35 SUVs, how many sedans do they have?
Solution (E):
Ratio \( \frac{\text{Sedan}}{\text{SUV}} = \frac{2}{5} \).
\( \frac{S}{35} = \frac{2}{5} \implies S = \frac{2}{5} \times 35 = 2 \times 7 = 14 \).
7.
A piggy bank contains pennies, nickels, and dimes. The ratio of pennies to nickels is 2:3 and the ratio of nickels to dimes is 4:5. What is the ratio of pennies to dimes?
Solution (B):
\(P:N = 2:3\) and \(N:D = 4:5\).
Make the \(N\) term equal in both. LCM of 3 and 4 is 12.
\(P:N = 8:12\) (Multiply by 4).
\(N:D = 12:15\) (Multiply by 3).
So \(P:N:D = 8:12:15\).
Ratio \(P:D = 8:15\).
8.
A $1000 prize is split among three winners in the ratio 5:3:2. What is the amount of the smallest prize?
Solution (D):
Total parts = \(5+3+2 = 10\).
One part = \(1000 \div 10 = 100\).
Smallest share = 2 parts = \(2 \times 100 = 200\).
9.
If 25% of \(x\) equals 15% of 1500, what is \(x\)?
Solution (A):
\(0.25x = 0.15 \times 1500\).
\(0.25x = 225\).
\(x = 225 \div 0.25 = 225 \times 4 = 900\).
10.
An item costing $200 is marked up by 50% and then sold at a 50% discount. What is the final selling price?
Solution (C):
1. Markup: \(200 \times 1.5 = 300\).
2. Discount: \(300 \times 0.5 = 150\).
The final price is $150.
Score: 0 / 0