Shortcut Trick
Original Ratio (Mobile : Standard : Premium) = 5 : 8 : 12
New Ratio units after changes: (5 − 10%) : 8 : (12 + 25%) = 4.5 : 8 : 15
Total new units = 4.5 + 8 + 15 = 27.5 units
Given: 27.5 units = 55,000 ⇒ 1 unit = 55,000 ÷ 27.5 = 2,000
Original Difference (Premium − Mobile) = 12 − 5 = 7 units ⇒ 7 × 2,000 = 14,000
∴ The correct answer is 14,000.
Alternate Method
Given:
Original ratio of Mobile, Standard, and Premium subscriptions = 5 : 8 : 12
New Total Subscriptions = 55,000
Calculations:
⇒ Let original subscriptions be 5x, 8x, and 12x.
⇒ Mobile (after 10% decrease) = 5x × 0.90 = 4.5x
⇒ Standard (unchanged) = 8x
⇒ Premium (after 25% increase) = 12x × 1.25 = 15x
⇒ New Total = 4.5x + 8x + 15x = 27.5x
⇒ 27.5x = 55,000
⇒ x = 55,000 ÷ 27.5 = 2,000
⇒ Original Premium Subscriptions = 12 × 2,000 = 24,000
⇒ Original Mobile Subscriptions = 5 × 2,000 = 10,000
⇒ Difference = 24,000 − 10,000 = 14,000
∴ The correct answer is 14,000.
Additional Information
Ratio and Proportion
When values are in a ratio a : b : c, they can be represented as ax, bx, and cx where x is the common multiplier.
Percentage Change
A decrease of 10% is equivalent to multiplying by 0.9 (1 − 0.1), and an increase of 25% is equivalent to multiplying by 1.25 (1 + 0.25).
Direct Variation
The difference between any two parts of a ratio scales linearly with the multiplier x. Difference = (Ratio1 − Ratio2) × x.