Question

A number is first increased by 40% and then decreased by 25%, again increased by 15% and then decreased by 20%, find the percentage of total increase or decrease in the number?

● (a) 7.2% decrease
● (b) 3.4% increase
● (c) 6.4% increase
● (d) 3.4% decrease


ANSWER IMMEDIATELY

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Answer 1

Let the number be x

⇒

$x \times \frac{7}{5} \times \frac{3}{4} \times \frac{23}{20} \times \frac{4}{5} \\ \\ = x \times \frac{483}{500} ..$

⇒ 0.966x

⇒ 0.966x is less than x

⇒ Decrease per cent in the number =

∴ Net decrease per cent in the number is 3.4%..

Answer 2

Answer:

(d) 3.4% decrease

Step-by-step explanation:

Let the number be 100.

• First increased by 40%.

⇒ 100 + 40% of 100

⇒ 100 + 40

⇒ 140

• Decreased by 25%.

⇒ 140 - 25% of 140

⇒ 140 - (25/100 × 140)

⇒ 140 - (1/4 × 140)

⇒ 140 - 35

⇒ 105

• Increased by 15%.

⇒ 105 + 15% of 105

⇒ 105 + (15/100 × 105)

⇒ 105 + (3/20 × 105)

⇒ 105 + (3/4 × 21)

⇒ 105 + (63/4)

⇒ 105 + 15.75

⇒ 120.75

• Decreased by 20%.

⇒ 120.75 - 20% of 120.75

⇒ 120.75 - (20/100 × 120.75)

⇒ 120.75 - (1/5 × 120.75)

⇒ 120.75 - 24.15

⇒ 96.6

• Net increase or decrease :

⇒ (96.6 - 100)/100 × 100

⇒ (96.6 - 100) %

⇒ -3.4%

Negative sign denotes the decrease.