120 practice questions covering Proportional Reasoning-1, organised into 0 topics.
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Sample questions
Q1
medium
Assertion (A): Walking at a steady $5\ \text{km/h}$ for $30$ minutes covers $2.5\ \text{km}$. Reason (R): Kilometres per hour is the unit normally used for the speed of vehicles on a highway.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: B - Both A and R are true, but R is not the correct explanation of A
Thirty minutes is half an hour, so the walker covers half of $5\ \text{km}$, which is $2.5\ \text{km}$, and A is true. R is a true statement about which unit is normally used for road speeds. Naming the usual unit does not explain the calculation in A, so R is not its reason.
Q2
medium
The scale of a map is $1\ \text{cm}$ to $250\ \text{km}$. A river is drawn $3.6\ \text{cm}$ long on this map. What is the real length of the river?
A$253.6\ \text{km}$
B$750\ \text{km}$
C$900\ \text{km}$
D$90\ \text{km}$
Show answer and explanation
Correct answer: C - $900\ \text{km}$
The real length is $3.6 \times 250 = 900\ \text{km}$. The answer $750\ \text{km}$ uses only the whole $3\ \text{cm}$ and drops the $0.6\ \text{cm}$. The answer $90\ \text{km}$ multiplies by $25$ instead of $250$, and $253.6\ \text{km}$ adds the two numbers instead of multiplying.
Q3
easy
A car travels $240\ \text{km}$ in $4$ hours. What is its average speed?
A$60\ \text{km/h}$
B$120\ \text{km/h}$
C$960\ \text{km/h}$
D$40\ \text{km/h}$
Show answer and explanation
Correct answer: A - $60\ \text{km/h}$
Average speed is distance divided by time, so it is $240 \div 4 = 60\ \text{km/h}$. The answer $40\ \text{km/h}$ divides by $6$ instead of $4$. The answer $120\ \text{km/h}$ halves the distance instead of quartering it, and $960\ \text{km/h}$ multiplies by $4$ rather than dividing.
Q4
easy
Are the ratios $6 : 10$ and $9 : 15$ equivalent?
ANo, because $9$ is not a multiple of $6$
BNo, because all four numbers are different
CNo, because $15 - 9$ is not equal to $10 - 6$
DYes, because both simplify to $3 : 5$
Show answer and explanation
Correct answer: D - Yes, because both simplify to $3 : 5$
Dividing $6 : 10$ by $2$ gives $3 : 5$, and dividing $9 : 15$ by $3$ also gives $3 : 5$, so the two ratios are equivalent. Equivalent ratios do not need matching numbers, one first term need not be a multiple of the other, and equal differences are not what makes ratios equal.
Q5
easy
Which unit is the most sensible for stating the distance by road between Delhi and Jaipur?
AKilometres
BCentimetres
CMillimetres
DMetres
Show answer and explanation
Correct answer: A - Kilometres
The distance is a few hundred kilometres, so kilometres keep the number short and easy to read. Metres would need a six-figure number, centimetres eight figures and millimetres nine, so all three make the measurement harder to read without making it any more useful.
Q6
easy
Which is the greater ratio, $3 : 4$ or $5 : 8$?
AThey are equal
BIt cannot be decided without more information
C$3 : 4$
D$5 : 8$
Show answer and explanation
Correct answer: C - $3 : 4$
Writing both as fractions with denominator $8$ gives $\frac{6}{8}$ and $\frac{5}{8}$, so $3 : 4$ is the greater ratio. The ratio $5 : 8$ is therefore the smaller of the two. They are clearly not equal, and any two ratios of whole numbers can always be compared in this way.
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