Successive percentage change in one step: a + b + ab/100

लगातार प्रतिशत बदलाव एक कदम में: a + b + ab/100

Two percentage changes one after another combine into a + b + (a × b ÷ 100). Use a minus sign for a decrease. Works for price rise and fall, population, discounts and area changes.

दो लगातार प्रतिशत बदलाव मिलकर a + b + (a × b ÷ 100) होते हैं। कमी के लिए ऋण (−) चिह्न लगाएँ। कीमत, जनसंख्या, छूट और क्षेत्रफल के सवालों में काम आता है।

The formula

Net change % = a + b + (a × b) ÷ 100. Take an increase as positive and a decrease as negative.

Add the two changes: a + b.
Add their product divided by 100.
A positive answer is a net increase, a negative answer a net decrease.

Example Price up 20%, then up 10%.

20 + 10 + (20 × 10 ÷ 100) = 32% increase

Example Price up 20%, then down 10%.

20 − 10 + (20 × −10 ÷ 100) = 10 − 2 = 8% increase

Example Two discounts of 10% each.

−10 − 10 + (100 ÷ 100) = −19 → single discount of 19%

Area and rectangle questions

If the length rises by a% and the breadth by b%, the area changes by the same formula, because area = length × breadth.

Example Length +25%, breadth −20%. Change in area?

25 − 20 + (25 × −20 ÷ 100) = 5 − 5 = 0 → no change

Successive discounts

Discounts of 20% and 10% are a single discount of 28%, not 30%. So ₹1,500 with 20% + 10% off costs 1,500 × 0.72 = ₹1,080.

Try it yourself · अभ्यास

Two discounts of 30% and 20%. Single equivalent discount?
Show answer
−30 − 20 + 600 ÷ 100 = −44 → 44%
Population falls 10% three years in a row. Overall change?
Show answer
0.9 × 0.9 × 0.9 = 0.729 → 27.1% decrease