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kanikaa9
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A certain quantity is measured on two different scales, the R-scale 18 Jan 2025, 10:29
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Scale R: Jump from 6 to 24 is an increment of 18, next would be 42 (24+18) (since it is given linear)
Scale S: Jump from 30 to 60 is an increment of 30, next would be 90 (60+30) (since it is given linear)

Now 100 on Scale S is 90 + 10 i.e. 1/3 of the increment (30/3)
So 1/3 of increment of Scale R is 18/3 = 6

Hence equivalent of 100 on Scale R would be 42 + 6 = 48 (C)
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A certain quantity is measured on two different scales, the R-scale 14 Apr 2025, 22:06
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QS says 6 and 24 correspond to 30 and 60 .. That means that 18 difference on R scale would give 30 difference on S scale . 1 unit on R scale is 5/3 on S scale . Now 40 difference(100 on S Scale - 60 on S Scale) on S scale would give 40/5/3 units of difference on R scale => 24 units of difference on R scale . So S scale value for 60 i.e 24 + difference of 24 =>48 units.
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File comment: QS says 6 and 24 correspond to 30 and 60 .. That means that 18 difference on R scale would give 30 difference on S scale . 1 unit on R scale is 5/3 on S scale . Now 40 difference(100 on S Scale - 60 on S Scale) on S scale would give 40/5/3 units of difference on R scale => 24 units of difference on R scale . So S scale value for 60 i.e 24 + difference of 24 =>48 units.
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A certain quantity is measured on two different scales, the R-scale 30 May 2025, 02:39
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If you know one of the straight lines equations:
y-y1=(y2-y1/x2-x1) x-x1,

treat the given values as x and y co-ordinate since they are related linearly,
x1,y1=6,30
x2,y2=24,60,

find the equation of line and insert the values you want to find out such as keep 100 in place of y and get the x value which will be 48.


appy001
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

(A) 20
(B) 36
(C) 48
(D) 60
(E) 84

PS02404
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A certain quantity is measured on two different scales, the R-scale 06 Oct 2025, 06:36
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I can see why this problem might feel tricky at first - when you see "related linearly," it's easy to overthink what that means. Let me walk you through this in a way that'll make it click.

Here's how to think about this:

Step 1: Understand what "linearly related" means

When two scales are linearly related, they follow a straight-line relationship. Think of it like the connection between Celsius and Fahrenheit - there's a predictable pattern. You're given two points:
  • When \(R = 6\), then \(S = 30\)
  • When \(R = 24\), then \(S = 60\)

Your goal: Find \(R\) when \(S = 100\).

Step 2: Find the rate of change (slope)

Let's see how both scales change together:
  • R increases from 6 to 24 → that's an increase of 18
  • S increases from 30 to 60 → that's an increase of 30

So the rate of change is \(\frac{30}{18} = \frac{5}{3}\)

This means: for every 3 units R increases, S increases by 5 units.

Step 3: Build the complete equation

Here's the key insight - a linear relationship isn't just about the slope. It follows the pattern: \(S = \frac{5}{3} \times R + \text{constant}\)

To find that constant, plug in one of your known points. Using \(R = 6\) and \(S = 30\):

\(30 = \frac{5}{3} \times 6 + \text{constant}\)
\(30 = 10 + \text{constant}\)
\(\text{constant} = 20\)

So your complete equation is: \(S = \frac{5}{3}R + 20\)

Quick verification with the second point \((R = 24, S = 60)\):
\(S = \frac{5}{3} \times 24 + 20 = 40 + 20 = 60\) ✓

Step 4: Solve for R when S = 100

Now substitute \(S = 100\):

\(100 = \frac{5}{3}R + 20\)
\(80 = \frac{5}{3}R\)
\(R = 80 \times \frac{3}{5} = \frac{240}{5} = 48\)

Answer: C (48)

The biggest trap here? Many students assume it's just a simple ratio problem and try something like \(R \times 5 = S\), forgetting that linear relationships include that constant term (+20 in this case). That's what makes the difference!

Want to master this systematically?

The approach I showed you works, but there's actually a more sophisticated framework for tackling all linear relationship problems efficiently. The complete solution on Neuron shows you the strategic approach that works across different variations of this question type, plus the time-saving patterns that help you spot the right setup instantly. You can check out the detailed explanation on Neuron to see the full framework and understand how this pattern applies to other problems. You can also explore comprehensive solutions for similar official questions on Neuron with practice quizzes that help you build consistent accuracy on these concepts.

Hope this helps!
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A certain quantity is measured on two different scales, the R-scale 29 Mar 2026, 08:43
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For every 18 increase in R, 30 increase in S.

Consider each unit to be 1 for S, then 18/30 = 3/5 units in R.

When we move from 60 to 100 in S, we jump by 40.
Meaning we jump 40*3/5 in S = 24.

We move from 24 and jump 24 more places = 24+24=48.

Answer: Option C
appy001
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

(A) 20
(B) 36
(C) 48
(D) 60
(E) 84

PS02404
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A certain quantity is measured on two different scales, the R-scale 23 Jul 2026, 23:59
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How I did the question was:

R ---- S
6 ---- 30
24 ---- 60, there is a gap of 18 (R) and 30 (S), if we add another 18 (R) and 30 (S) then we get

42 ---- 90, we understand that we have +18 (R) for +30 (S), so a +10 (S) would mean a +6 (R)
48 ---- 100

Please let me know if this understanding is correct.
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A certain quantity is measured on two different scales, the R-scale 28 Jul 2026, 11:01
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Hi Rishab2409,

Your method is completely valid, and it lands on the right answer for the right reason. Let me walk through why each step holds.

You started from the two given points and used the fact that the relationship is linear, which means equal jumps in R always produce equal jumps in S:

- 6 - 24 in R matches 30 - 60 in S, so +18 in R = +30 in S.
- Adding one more identical step: 24 - 42 in R matches 60 - 90 in S.

That's the key insight - because the relationship is a straight line, you can keep stepping by the same fixed amount and stay on it. So far, perfect.

The last move is the one worth pausing on, because it's where students sometimes get nervous: you needed to go from 90 to 100 in S, a jump of only +10 - not a full +30. You scaled the step down proportionally: since +30 in S = +18 in R, a +10 in S (one-third of 30) means +6 in R (one-third of 18). So 42 - 48.

That proportional scaling of a partial step is exactly what "linear" lets you do - the ratio of change stays constant no matter how big or small the jump. 48 is correct.

One thing to keep in your back pocket: your table approach works beautifully here because the numbers land on clean fractions (100 sat neatly at 90 + one-third of a step). When the target doesn't fall on a tidy multiple, the same idea still works - just lean directly on the rate: every +1 in S = +18/30 = +3/5 in R. From 60 to 100 is +40 in S, so +40 × 3/5 = +24 in R, giving 24 + 24 = 48. Same answer, same logic, no table needed.

Your understanding is spot on - trust it.

Answer: C

Rishab2409
How I did the question was:

R ---- S
6 ---- 30
24 ---- 60, there is a gap of 18 (R) and 30 (S), if we add another 18 (R) and 30 (S) then we get

42 ---- 90, we understand that we have +18 (R) for +30 (S), so a +10 (S) would mean a +6 (R)
48 ---- 100

Please let me know if this understanding is correct.
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