Two numbers are in the ratio 5 ∶ 8. If the first number increases by 40% and second number decreases by 15%, the new ratio becomes ______.
- AOption (a)
37 ∶ 39
- BOption (b)
35 ∶ 34
- COption (c)
12 ∶ 17
- DOption (d)
23 ∶ 26
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Correct answer
35 ∶ 34
Why this answer is correct
Shortcut Trick
Multiply the ratio terms directly by their respective percentage change factors.
New First Number = 5 × 140% = 7.0
New Second Number = 8 × 85% = 6.8
New Ratio = 7.0 : 6.8 → 70 : 68 = 35 : 34.
∴ The correct answer is 35 : 34.
Alternate Method
Given:
Initial Ratio of two numbers = 5 : 8
Percentage Increase in first number = 40%
Percentage Decrease in second number = 15%
Formula Used:
New Value = Original Value × (100 ± Change%)/100
Calculations:
Let the two numbers be 50x and 80x respectively.
⇒ First number after 40% increase = 50x × (140/100) = 70x
⇒ Second number after 15% decrease = 80x × (85/100) = 68x
⇒ New Ratio = 70x : 68x
⇒ New Ratio = 70 : 68
⇒ Dividing both terms by 2:
⇒ New Ratio = 35 : 34
∴ The correct answer is 35 : 34.
Additional Information
Concept of Multiplier
For an increase of x%, multiply the base value by (1 + x/100). For a decrease of x%, multiply by (1 − x/100).
Simplifying Ratios
A ratio a : b remains unchanged if both terms are multiplied or divided by the same non-zero constant k.
Successive Percentage Change
If a value changes by a% and then by b%, the net change is [a + b + (a × b)/100]%.