A class has boys and girls in an 11:13 ratio. After 8 girls and 4 boys join this term, the ratio becomes 4:5. Find the total class size.
Show answer Hide answer
Answer: D. 108
Explanation
Let the initial number of boys be eleven x and girls be thirteen x based on the given ratio. After adding four boys and eight girls, the new ratio of boys to girls is set equal to four over five. Solving this linear equation yields x equal to four, which means the total class size is twenty four times four plus twelve, equaling one hundred eight. Ratios express the relative sizes of two or more values using proportional multipliers. Algebraic equations allow solving for unknown multipliers when quantities are changed by fixed amounts. Total class size is found by summing the updated counts of both boys and girls.
Option A overestimates the total class size based on an incorrect algebraic multiplier. Option B underestimates the class size and fails the ratio equality test after additions. Option C is incorrect because the solved value of x produces a different total enrollment number.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A rectangular field has a 5:4 length-to-breadth ratio. If breadth is 20 meters less than length, what is the field's perimeter_________?
Show answer Hide answer
Answer: C. 360m
Representing length and breadth with variables based on a five-to-four ratio sets up a solvable linear equation. Solving the difference equation yields a multiplier value of twenty for both rectangular dimensions. Calcul...
Q2. A cylinder's radius is half its height, and its inner surface area is 616 sq cm. Approximately how many litres of milk can it hold?
Show answer Hide answer
Answer: B. 1.5
Using the curved surface area formula and the relation radius equals height over two allows finding dimensions. Solving the surface area equation yields specific radius and height values for the cylindrical container. Ca...
Q3. In what ratio should rice priced at Rs. 7.20 per kg be blended with rice at Rs. 5.70 per kg to yield a mixture worth Rs. 6.30 per kg_________?
Show answer Hide answer
Answer: B. 2:3
By alligation the ratio is the difference below the mean price to the difference above it, which is 6.30 minus 5.70 against 7.20 minus 6.30, or 0.60 to 0.90. That simplifies to 2 to 3, so two parts of the dearer rice to...
Q4. Partners P and Q invest in a 7:5 ratio and earn profits in a 7:10 ratio. If P invested for 5 months, for how long did Q invest?
Show answer Hide answer
Answer: B. 10 months
The partnership ratio calculation relies on equating the product of investment and time proportionally. Multiplying partner P investment by duration and dividing by partner Q product yields the correct ratio. Isolating t...
Q5. Two spheres have radii in a 1:3 ratio. Find the ratio of their volumes.
Show answer Hide answer
Answer: B. 1:27
The volume ratio of two similar three-dimensional spheres equals the cube of the ratio of their radii. Cubing the given radius ratio of one-third yields one over twenty-seven for the volumetric proportion. This mathemati...
Q6. Two numbers in a 3:4 ratio have an H.C.F of 4. What is their L.C.M__________?
Show answer Hide answer
Answer: D. 48
Multiplying the ratio terms three and four by the highest common factor four gives twelve and sixteen. Alternatively multiplying the ratio product by the HCF directly yields the least common multiple. Calculating three m...