Given below are two statements : Given that a: b=5: 3 and b: c=2: 5, then value of ( c-a ) will be equal to Statement I: 10(a+c) Statement II: 10 a+25 b In the light of the above statements, choose the correct answer from the options given below : Option 1: Both Statement I and Statement II are true Option 2: Both Statement I and Statement II are false Option 3: Statement I is true but Statement II is false Option 4: Statement I is false but Statement II is true

Answer: Both Statement I and Statement II are false. Solution: Let me solve this step by step. 1) Given ratios: * a:b = 5:3 * b:c = 2:5 2) From first ratio a/b = 5/3 * If we take b = 6 (to make calculations easier) * Then a = 10 * These values maintain the ratio 5:3 3) From second ratio b/c = 2/5 * With b = 6 * Then c = 15 * These values maintain the ratio 2:5 4) Now we can find (c-a): * c-a = 15-10 = 5 5) Let's check Statement I: * 10(a+c) * 10(10+15) * 10(25) * 250 This is not equal to (c-a) = 5 6) Let's check Statement II: * 10a+25b * 10(10)+25(6) * 100+150 * 250 This is not equal to (c-a) = 5 Therefore, both statements are false.

Arithmetic

Ratio, Proportion & Variation

Easy

Given below are two statements :

Given that $a: b=5: 3$ and $b: c=2: 5$ , then value of ( $c-a$ ) will be equal to

Statement I: $10(a+c)$

Statement II: $10 a+25 b$

In the light of the above statements, choose the correct answer from the options given below :

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

✅ Correct Option: 2

Let me solve this step by step.

Given ratios:

$a:b = 5:3$ $a : b = 5 : 3$
- $b:c = 2:5$

From first ratio $\frac{a}{b} = \frac{5}{3}$

If we take $b = 6$ $b = 6$ (to make calculations easier)
- Then $a = 10$
- These values maintain the ratio $5:3$

From second ratio $\frac{b}{c} = \frac{2}{5}$

With $b = 6$ $b = 6$
- Then $c = 15$
- These values maintain the ratio $2:5$

Now we can find $(c-a)$ :

$c-a = 15-10 = 5$

Let's check Statement I:

$10(a+c)$ $10 (a + c)$
- $10(10+15)$
- $10(25)$
- $250$

This is not equal to $(c-a) = 5$

Let's check Statement II:

$10a+25b$ $10 a + 25 b$
- $10(10)+25(6)$
- $100+150$
- $250$

This is not equal to $(c-a) = 5$

Therefore, both statements are false.

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Choose the correct answer from the options given below:

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