WORKSHEET ON PERCENTAGE PROBLEMS

Question 1 :

Before a big test, James memorized 10 percent more words 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?

Question 2 :

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 1,200 calls, how many calls does Call center C handle?

Question 3 :

If X is 20% of Y and Y is 30% of Z, then what percent of Z is X?

Question 4 :

The price of a text book this year is 20% greater than the price last year. If this year's price is p, what was last year's price in terms of p?

Question 5 :

A cylinder has a base radius of r and a height of h. If the radius is reduced by 30%, how would the volume of the cylinder change?

1. Answer :

Given : Amy memorized a words and Zach memorized 30 percent more words than Amy.

Number of words memorized by Zach :

= (100 + 30)% of a

= 130% of a

= (1.30)a

Given : James memorized 10 percent more words than Zach.

Number of words memorized by James :

= (100 + 10)% of (1.30)a

= 110% of (1.30)a

= (1.10)(1.30)a

2. Answer :

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 1,200 calls, how many calls does Call center C handle?

Let x be the number of calls handles by Call center C.

Given : Call center B handles 20% fewer calls than Call center C.

Number of calls handled by Call center B :

= (100 - 20)% of x

= 80% of x

= 0.8x

Given : Call center A handles 20% fewer calls than Call center B.

Number of calls handled by Call center A :

= (100 - 20)% of 0.8x

= 80% of 0.8x

= (0.8)(0.8x)

= 0.64x

Given : Call center A handles 1200 calls.

0.64x = 1200

Divide both sides by 0.64.

x = 1875

Call center C handles 1875 calls.

3. Answer :

If X is 20% of Y and Y is 30% of Z, then what percent of Z is X?

Given : X is 20% of Y.

X = 0.2Y

Divide both sides by 0.2.

5X = Y

Given : Y is 30% of Z.

Y = 0.3Z

Substitute Y = 5X.

5X = 0.3Z

Divide both sides by 5.

X = 0.06Z

X = (6/100)Z

X = 6% of Z

6% of Z is X.

4. Answer :

Let x be the price of the text book last year.

Given : The price of a text book this year is 20% greater than the price last year.

This year's price = (100 + 20)% of x

= 120% of x

= 1.2x

Given : This year's price is p

1.2x = p

Divide both sides by 1.2.

x = (1/1.2)p

x = (10/12)p

x = (5/6)p

5. Answer :

Volume of a cylinder base radius of r and a height of h :

πr2h

If the radius is decreased by 30%, then the new radius is 

= (100 - 30)% of r

= 70% of r

= 0.7r

Volume of the cylinder after the radius is reduced by 30% :

π(0.7r)2h

π(0.49r2)h

= 0.49(πr2h)

= (49/100)(πr2h)

= 49% of (πr2h)

100 - 49 = 51

Volume of the cylinder would decrease by 51%.

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