1. Increase $5000 by 20%.
2. Decrease $85 by 22%.
3. Increase 78 kg. by 3%.
4. Increase 800 m by 15%
5. What is the overall effect of increasing $100 by 10% and then decreasing the result by 10%?
6. When decreasing a quantity by 10% in two successive years, the overall result is to decrease the original by 19%, verify.
7. Find the overall effect of increasing a quantity by 20% each year for 3 successive years.
8. Increase 150 by 10% and decrease the same by 15%. Find the new number in each case.
9. A product has been priced $80. If the product is sold on 20% discount, how much has to be paid for the product?
10. The price of a garment is $90 and now it is on a sale of 10% off. If there is a sales tax of 5%, how much has to be paid for the garment?
11. A value is increased by 20%. If the value after increase is 96, find the original value.
12. The sale price of a car is $12,590, which is 20% off the original price. What is the original price?
1. Answer :
= (100 + 20)% of 5000
= 120% of 5000
= (120/100) x 5000
= 1.20 x 5000
= 6000
When $5000 is increased by 20%, it is $6000.
2. Answer :
= (100 - 22)% of 85
= 78% of 85
= (78/100) x 85
= 0.78 x 85
= 66.3
When $85 is increased by 22%, it is $66.30.
3. Answer :
= (100 + 3)% of 78
= 103% of 78
= (103/100) x 78
= 1.03 x 78
= 80.34
When 78kg. is increased by 3%, it is 80.34 kg.
4. Answer :
= (100 + 15)% of 800
= 115% of 800
= (115/100) x 800
= 1.15 x 800
0= 920
When 800 m. is increased by 15%, it is 920 m.
5. Answer :
Increase $100 by 10%.
= (100 + 10)% of 100
= 110% of 100
= (110/100) x 100
= 110
When $100 is increased by 10%, it is $110.
Decrease $110 by 10%.
= (110 - 10)% of 110
= 90% of 110
= (90/100) x 110
= 0.9 x 110
= 99
When $110 is decreased by 10%, it is $99.
After the two changes (10% increase and 10% decrease), the original amount $100 becomes $99.
The original quantity 100 is decreased by 1.
Therefore, the overall effect is 1% decrease.
6. Answer :
Let the original quantity be 100.
Decrease 100 by 10%.
= (100 - 10)% of 100
= 90% of 100
= (90/100) x 100
= 0.9 x 100
= 90
Decrease 90 by 10%.
= (100 - 10)% of 90
= 90% of 90
= (90/100) x 90
= 0.9 x 90
= 81
When decreasing by 10% in two successive years, the original quantity 100 becomes 81.
Decrease 100 by 19% :
= (100 - 19)% of 100
= 81% of 100
= (81/100) x 100
= 0.81 x 100
= 81
In both ways, we get the same answer.
Decreasing a quantity by 10% in two successive years and decreasing the original quantity by 19% are equal.
7. Answer :
Let 100 be the original quantity.
Increase 100 by 20% :
= (100 + 20)% of 100
= 120% of 100
= (120/100) x 100
= 1.20 x 100
= 120
Increase 120 by 20% :
= (100 + 20)% of 120
= 120% of 120
= (120/100) x 120
= 1.20 x 120
= 144
Increase 144 by 20% :
= (100 + 20)% of 144
= 120% of 144
= (120/100) x 144
= 1.20 x 144
= 172.8
After increasing a quantity by 20% each year for 3 successive years, the original quantity 100 becomes 172.8
The original quantity 100 is increased by 72.8.
Therefore, the overall effect is 72.8% increase.
8. Answer :
Increase 150 by 10% :
= (100 + 10)% of 150
= 110% of 150
= (110/100) x 150
= 1.1 x 150
= 165
Decrease 150 by 10% :
= (100 - 10)% of 150
= 90% of 150
= (90/100) x 150
= 0.9 x 150
= 135
9. Answer :
Price of the product after 20% discount :
= (100 - 20)% of 80
= 80% of 80
= (80/100) x 80
= 0.8 x 80
= 64
$64 has to be paid for the product.
10. Answer :
Price of the product after 10% off :
= (100 - 10)% of $90
= 90% of $90
= (90/100) x 90
= 0.9 x 90
= $81
Increase 81 by 5% (sales tax).
= (100 + 5)% of 81
= 105% of 81
= 1.05 x 81
= 85.05
$85.05 has to paid for the garment.
11. Answer :
Let A be the original value.
The value after increased by 20% is 96.
(100 + 20)% of A = 96
120% of A = 96
1.2A = 96
Divide both sides by 1.2.
A = 80
12. Answer :
Let A be the original price of the car.
The sale price of a car is $12,590, which is 20% off the original price.
That is, when the original price is decreased by 20%, we will get the sale price which is $12,590
(100 - 20)% of A = 12590
80% of A = 12590
0.8A = 12590
Divide both sides by 0.8.
A = 15737.50
The original price of the car is $15,737.50.
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