Proportional Reasoning - 2 - Free MCQ Practice Test with solutions,

A proportional relationship occurs when two or more quantities change by the same factor, which can be represented using ratios. For example, if the ratio of flour to sugar is maintained while increasing the quantities, this indicates proportionality.

In the ratio 1 : 1.5 : 3, the 3 parts represent 110 units of concrete. One part = 110 ÷ 3 ≈ 36.67 units. Sand corresponds to 1.5 parts, so sand required = 1.5 × 36.67 ≈ 55 units.

Total parts = 2 + 1 = 3.

One part = 12 ÷ 3 = 4.

Therefore the parts are 2 × 4 = 8 and 1 × 4 = 4.

Since the ratio is 2:1, the first part is 8 and the second is 4.

The total ratio is 1 + 2 + 3 = 6. To find the parts for 90 units, divide 90 by 6 to get 15. Therefore, the first component (1 part) will be 1 x 15 = 15 units.

Sum of ratio parts = 1 + 1.5 + 3 = 5.5.

Given cement corresponds to 1 part and actual cement = 3 bags, scale factor = 3 ÷ 1 = 3.

Total bags = 5.5 × 3 = 16.5 bags.

Interpret the ratio as red : blue : white = 2 : 3 : 5, so white corresponds to 5 parts and equals 10 litres.

One part = 10 ÷ 5 = 2 litres.

Red = 2 parts = 2 × 2 = 4 litres.

Representative Fraction (RF) is the ratio of a distance on the map to the corresponding distance on the ground.

RF = 1 : 60,000,000 means 1 unit on the map = 60,000,000 same units on the ground.

Thus, 1 cm on the map = 60,000,000 cm on the ground = 600 km on the ground.

Therefore, option C is correct.

Sum of ratios = 6 + 5 + 4 + 3 + 2 = 20.

Fraction for the category with ratio 6 = 6/20 = 3/10.

Angle = (3/10) × 360° = 108°.

Two quantities are inversely proportional if their product remains constant. For example, if one quantity increases, the other decreases, keeping their product constant.

Ram's rate = 1 job per 1 hour = 1 job/hr. Shyam's rate = 1 job per 1.5 hours = 1 / 1.5 = 2/3 job/hr.

Combined rate = 1 + 2/3 = 5/3 job/hr.

Time = 1 job ÷ (5/3 job/hr) = 3/5 hr.

Convert to minutes: (3/5)×60 = 36 minutes. Hence they take 36 minutes.

Sum of ratio parts = 1 + 3 + 5 = 9.

Each part measures 180° ÷ 9 = 20°.

Smallest angle = 1 × 20° = 20°.

Work is proportional to workers × time, so total work (in worker-days) is constant.

Total work = 5 × 10 = 50 worker-days.

With 10 workers, time = 50 ÷ 10 = 5 days.

Answer: 5 days.

Inverse proportion ⇒ x × y = constant
4 × 12 = 48
When x = 6:
y = 48 ÷ 6 = 8

Two pumps together fill 1 tank in 18 hours; their combined rate is 1/18 tank per hour.

Rate of one pump = (1/18) ÷ 2 = 1/36 tank per hour.

Rate of four pumps = 4 × 1/36 = 1/9 tank per hour.

Time for four pumps = reciprocal of rate = 9 hours.

Let the parts be 3x, 4x and 5x.
Given: 4x − 3x = x = 80 ⇒ x = 80.
So the parts are 240, 320 and 400.
Largest part = 5x = 5 × 80 = ₹400.