Calculate the least whole number, which when subtracted from both the terms of the ratio 5 : 6 gives a ratio less than 17 : 22.a)5b)3c)2d)4Correct answer is option 'C'. Can you explain this answer?

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Calculate the least whole number, which when subtracted from both the terms of the ratio 5 : 6 gives a ratio less than 17 : 22.

a)
5
b)
3
c)
2
d)
4

Correct answer is option 'C'. Can you explain this answer?

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Verified Answer

Calculate the least whole number, which when subtracted from both the ...

Given:

Initial ratio = 5 ∶ 6

Final ratio should be less than 17 ∶ 22

Calculation:

Let the least whole number that is needed to be subtracted be a.

According to the question,

(5 - a)/(6 - a) < 17/22

⇒ 5 × 22 - 22a < 17 × 6 - 17a

⇒ 110 - 22a < 102 - 17a

⇒ 110 - 102 < - 17a + 22a

⇒ 8 < 5a

⇒ 8/5 = 1.6 < a

∴ The least whole number must be 2.

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Most Upvoted Answer

Calculate the least whole number, which when subtracted from both the ...

Given:

Initial ratio = 5 ∶ 6

Final ratio should be less than 17 ∶ 22

Calculation:

Let the least whole number that is needed to be subtracted be a.

According to the question,

(5 - a)/(6 - a) < 17/22

⇒ 5 × 22 - 22a < 17 × 6 - 17a

⇒ 110 - 22a < 102 - 17a

⇒ 110 - 102 < - 17a + 22a

⇒ 8 < 5a

⇒ 8/5 = 1.6 < a

∴ The least whole number must be 2.

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Calculate the least whole number, which when subtracted from both the ...

To find the least whole number that, when subtracted from both terms of the ratio 5:6, gives a ratio less than 17:22, we can follow these steps:

Step 1: Simplify the given ratios
The given ratio is 5:6. We can simplify this ratio by dividing both terms by their greatest common divisor (GCD), which is 1 in this case. So, the simplified ratio is still 5:6.

Similarly, the second ratio 17:22 can also be simplified by dividing both terms by their GCD, which is 1. So, the simplified ratio is still 17:22.

Step 2: Find the difference between the two ratios
To find the difference between the two ratios, we subtract the terms of the first ratio from the terms of the second ratio. The difference is:

(17 - 5) : (22 - 6) = 12:16

Step 3: Simplify the difference ratio
Next, we simplify the difference ratio by dividing both terms by their GCD, which is 4. So, the simplified difference ratio is:

12 ÷ 4 : 16 ÷ 4 = 3:4

Step 4: Determine the least whole number
To find the least whole number that, when subtracted from both terms of the original ratio 5:6, gives a ratio less than 17:22, we need to find the difference between the original ratio and the difference ratio.

5:6 - 3:4 = (5 - 3) : (6 - 4) = 2:2

Since the resulting ratio is 2:2, which is equivalent to 1:1, we can conclude that the least whole number that satisfies the given condition is 1.

However, the options provided in the question do not include 1. So, we can assume that the question intends to find the least positive whole number. In this case, the least positive whole number that satisfies the given condition is 1.

Therefore, the correct answer is option C) 1.

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