PERCENTAGE INCREASE AND DECREASE QUESTIONS AND ANSWERS FOR SAT

Problem 1 :

Before a big test, James memorized 10 percent more word than Zach. Zach memorized 30 percent more words than Amy. If Amy memorized a words, how many words did James memorize in terms of a ?

a) 1.10 (1.30a)     b)  a/(1.10) (1.30)    c)  a/(0.9)(0.7

d)  1.40a 

Solution :

Number of words memorized by Amy = a

(should be considered as 100%)

Zach has memorized = 130% of a

James has memorized = 110 % of 130% of a

= 1.10(1.30a)

So, number of words James has memorized is 1.10(1.30a).

Problem 2 :

A grocery store has two recycling machines outside. The first recycling machine took in 240 plastic bottles and 180 metal cans. The second took in 30 percent more plastic bottles but 10 percent less metal cans. The second machine recycled what percent more items than the first (rounded to the nearest percent)

a)  9%     b) 11%     c)  13%     d)  15%

Solution :

Number of plastic bottles = 240

Number of metal cans = 180

Number of plastic bottles produced = 130% of 240

= 1.30 (240)

= 312

Number of metal cans = 90% of 180

= 0.90(180)

= 162

Approximately 13%, option c is correct.

Problem 3 :

The kinetic energy of an object is given by (1/2) mv², where m is the mass of the object and v is the velocity.

A radioactive element loses 15 percent of its mass and 20 percent of its velocity. By what percent has its kinetic energy decreased ?

Solution :

(1/2) mv²

New mass after 15 percent loss = 85% of m

New velocity after 20% loss = 80% of v

= (1/2) x 85% of m x (80% of v)²

= (1/2) x 0.85 m x 0.64 v²

= 0.544 (1/2) m v²

= 54.4% of (1/2) m v²

(100 - 54.4) = 45.6 % of kinetic energy is decreased.

Problem 4 :

Call center A handles 20% fewer calls than call center B. Call center B handles 20% fewer calls than call center C. If call center A handles 1200 calls, how many calls does call center C handle ?

Solution :

Number of calls handled by call center A = 1200

Number of calls handled by call center B = 120% of 1200

= 1.20(1200)

= 1440

Number of calls handled by call center C = 120% of 1440

= 1.20(1440)

= 1728

So, the number of calls handled by call center C is 1728.

Problem 5 :

Victor wants to sell 3 watches, each at the same price. After negotiation with customers however ends up selling one at 30% discount, one at 20% discount and one at 10% discount. If Victor sold the watches for a total of 240, how much money did he lose by giving the discounts ?

Solution :

Let x be the cost of one watch.

70% of x + 80% of x + 90% of x = 240

0.70x + 0.80 x + 0.90x = 240

2.4x = 240

x = 240/2.4

x = 100

Amount he losses = 30% of 100 + 20% of 100 + 10% of 100

= 100(0.30+0.20+0.10)

= 100(0.60)

= 60

So, he lost $60 by selling all these three watches by giving discounts.

Problem 6 :

If X is 20% of Y a nd Y is 30% of Z, what percent of Z is X ?

a)  5%     b)  6%      c) 8%     d)  12%

Solution :

X = 20% of Y ----(1)

Y = 30% of Z ----(2)

From (1), 

X = 0.20Y then Y = X/0.20

From (2)

Y = 0.30Z

Applying the value of Y, we get

X/0.20 = 0.30Z

Z = X/0.20 (0.30)

Z = X/0.06

Z = 6% of X

So, Z is 6% of X.

Problem 7 :

This year, Roger beat Rafael in 25% of their tennis matches. If Rafael won 18 matches, how many matches did Roger win ?

Solution :

Number of matches Rafael won = 18

Number of matches Roger won = 25% of 18

= 0.25 x 18

= 4.5

So, the number of matches Roger won is 4.

Problem 8 :

The price of a textbook this year is 20% greater than the price last year. If this year's price is p. What was the last year's price in terms of p ?

Solution :

Let x be the price of last year

This year's price = 120% of x

p = 120% of x

p = 1.20x

x = p/1.20

x = p(100/120)

x = p(5/6)

x = 5p/6

Problem 9 :

The original price of a suit is $1000. A sales man decides to discount it by 30%. Later on, the manager decides to give 15% discount off the sales man's price. What is the final price of the suit ?

a)  $350     b)  $485    c)  $550    d)  $595

Solution :

Original price = $1000

Price after discount = 70% of 1000

Amount that manager decides = 85% of (70% of 1000)

= 0.85(0.70 x 1000)

= 595

So, the final price is $595.

Problem 10 :

A large group of friends go out to dinner at a restaurant which charges them a service fee of 12 percent of the original price of their meal. After this fee is factored in the group uses a coupon to get 25 percent off the total. In the end, what percent discount did the group receive off the original price ?

Solution :

Let x be the original price 

Amount after service fee = 112% of x

Final amount = 75% of 112% of x

= 0.75(1.12x)

= 0.84 x

= 84% of x

discount  = 100% - 84%

= 16% is the discount.