Problem – Solving

1. Josef purchased a lawn mower which was sold at 20% discount. He paid Php 14,800.00 for the lawn mower. How much was the original price of the law mower?

1. Php 18,250

2. Php 18,565

3. Php 18,500

4. 18,575

Let X = original price of the lawn mower

20% = discount given Php 14,800.00 = net price paid

X – .20X = Php 14,800.00

__.80X__= Php

__14,800__

.80 .80

x = Php 18,500.00

P 18,500 – .20 ( P 18.500 ) = P14,800

P 18,500 – P 33,700 = P14,800

P14,800 = P14,800

Ans: 3

2. Ruth is paid P 17,000 for regular 40hr. week. Up to 40 hours, she is paid at the regular hourly rate. For overtime of more than 40 hrs, she receives 11 ½ times as much as the regular hourly rate. How many hours did she work during a particular week when she earned about P 24,650.00 ?

1. 48 hrs

2. 52 hrs

3. 55 hrs

4. 54 hrs

Ruth’s regular rate per hour. = P17,000 / 40 hrs = P 425.00 per hr.

Ruth’s overtime rate per hour: Regular x 1.5 = P 425.00 x 1.5 = P 637.50

Ruth’s overtime pay: P 24,650 – P 7,650

Ruth’s overtime pay per hour: P 7,650 / P 637.50 = 12 hrs

Regular work week + overtime : 40 hrs = 52 hrs.

Ans: 2

3. A stationery pad that sells for P 18.50 can be bought for for P 150 when a dozen pads are purchased at one time. What is the savings per pad, in pesos, when the pads are purchased by the dozen?

1. P 6.95

2. P 6.50

3. P 6.75

4. P 6.00

P 150.00 / 12 = p 12.50 per pad

P 18.50 – P 12.50 = P 6.00

Ans: 4

4. On the day of the school concert, 500 tickets were sold. The students paid P150 each while non-students paid P200 each. If the total of P85,000 was collected, how many non-students attended?

1. 250

2. 230

3. 260

4. 200

Money collected = P85,000 # of tickets sold = 500 tickets

Let X = number of students Let Y = number of non-students

X + Y = 500

150X + 200Y = P 85,000

( X + Y = 500 ) 150 check: X + 200 = 500

150X + 200Y = 85.000 X = 500 – 200

150X + 150 Y = 75.000 X = 300

150X – 200 Y = 85.000

– 50 Y = 10.000

Y = 200

Ans: 4

5. A faucet filled a 315 gallon tank in 9 hrs. Later, the tank suffered a crack at the bottom and started leaking at the rate of 6 gallons/hr. How long will it takes the faucet to refill the emptied tank?

1. 11 hrs and 29 mins

2. 11 hrs

3. 10 hrs and 48 mins

4. 13 hrs

315b/9t – 6/1

35 T – 6T = 31

29T / 29 = 315 / 29

T = 10 hrs and 89 mins

= 10 hrs and 1 hr and 29 mins

= 11 hrs and 29 mins

Ans: 1

6 . Josef Raymund divided his estate among his three children: Joe, Ray and Sef in the ratio of 3: 2 : 2. If Sef received the amount of P 2.85M, what was the total estate ?

1. P 10M

2. P 9.975M

3. P 9.5M

4. P9.9M

P 2,850,000 / 2 = P 1,425 Joe : 3 ( P1,425,000 ) = P 4,275,000

Ray : 2 ( P1,425,000 ) = p 2,850,000

Sef : 2 ( P 1,425,000 )

Total = P 9,975,000

Ans: 2

7. The Del Rosario family’s monthly income is P 25,000. The family spends 30% for food, 20% FOR rentals, 10% for clothing ans 16% for miscellaneous. How much is saved in peso value?

1. P6,520

2. P6,250

3. P6,000

4. P6,400

solution: 30% + 20% + 10% + 16% = 76%

P25,000 x 76 / 100 = P1,900,000 / 100 = P 19,000

P25,000 – P19,000 = 6,000

Ans: 3

8. A motorcycle covers 225kms in 2 ½ hrs. How far can he go in 1 ¾ hrs?

1. 158 kms

2. 157.5 kms

3. 150 kms

4. 165 kms

solution:

__225 kms__=__2.5 hrs__2.5hrs. N = 225 (1.75) N 1.75 hrs

__2.5hrsN__=__393.75__ 2.5 2.5

N = 157.5 kms

Ans: 2

9. One way fare from Manila to Davao is P5,200. How many round trip tickets can be purchased with the amount of P104.000?

1. 11

2. 10

3. 12

4. 9

solution: P5,200 x 2 = P10,400 round trip fare

P104,000 / p10,400 = 10 round trip tickets

Ans: 2

10. Mr. Sison left his house at 7:00am and drove his car at 50kph. He rested for half an hour. What time he reach his destination which is 600kms away?

1. 7:30pm

2. 7:00pm

3. 8:00pm

4. 8:30pm

solution: speed = distance / time

__ST = D__ S S

T = D / S T = 600 / 50 T = 12 hrs + 30 mins (rest time)

T = 7: 30 PM

Ans: 1

11. Ruth bought 55 copies of Phil. History and paid a total of p3,850.00. if she buys 3 copies more of the same book, how uch will she pay in all?

1. P4,060

2. P4,260

3. P4,160

4. P4,150

Solution: P3,850 / 55 copies = p70.00 per copy.

P 70.00 x 3 more copies = P210.00

P 3,850 210.00 = P4,060 total cost for 58 books

Ans: 1

12. A manufacturer finds that 150 pieces of pens are defective and unsuitable for sale. If the defective pens are equivalent to three percent of the production, how many pens are being produced?

1. 5,100

2.

3. 5,000

4. 5,150

solution: Let X = no. of pens produced

3% = percentage of defective pens in proportion to production

150 = no. of defective pens

3%X = 150 ; 3% X = or 150/3% or 150/.03

X = 5,000

Ans: 3

13. Timmie owns 40% of the stock in millennium Traders, Inc. Jsef owns 15,000

shares. Bernice owns all the shares not owned by Timmie nor Josef. How many shares does Timmie own if Bernice has 25% more shares than Timmie?

1. 45,000 shares

2. 50, 000 shares

3. 60,00 shares

4. 75,000 shares

Solution: Timmie = 40% Millenium Traders

Bernice = owns 25% more than Timmie’s share in the Company

Josef = owns shares neither owned by Timmie’s nor Bernice

= 100% – 40% – 50% – 10%

I f Josef owns 10% of Millennium equivalents to 15,000 shares,

then Let X = 15,000 /.10

X = 150,000 thus : Timmie owns : 40% X 150,000

= 60.000

Ans: 3

14. Mang Lorenzo, a gardener, can now a lawn in 3hrs. After 2 hrs, it raned and he stopped moving the lawn. In the afternoon. Aling Tina, completed the rest of the word in one hour and 30 minutes. How long would it takes Aling Tina to mow the lawn by herself?

1. 1 hr and 30 mins.

2. 2 hrs and 22 mins.

3. 2 hrs

4. 2 hrs and 30 mins.

solution: Part of work done =

__time actually spent working__ time required to accomplish work

Let X # of hours it would take Aling Tina to mow the lawn by herself.

Mang Lorenzop = 2/3 of the work done in hrs.

Aling Tina = 1 ½ hrs to finish the rest of the work. 3/2 or ½

= 3/2X = Part of the work done by Aling Tina

= 2/3 + 3 / 3X = 1

3/2X = 1/3 / 3/2

X = 2/9 or 2.22

Ans: 2

15. A couple wants to have only four children so spaced that the first is older than the second by 2 years, the second older than the third by three years, the third older than the fourth by 4 years. If their plan is realized, how old will the eldest child be when the youngest is nine years old?

1. 18 yrs. Old

2. 9 yrs. Old

3. 16 years old

4. 17 years old

5. 18 years

Solution: Let X = age of the eldest by the time the younest is nine years. Old

2 ÷ 3 + 4 = total no. of years.

9 = total no. of age difference.

If the youngest would be 9 years old, adding the no. of age

Difference: X + 9 years = 18 years old

Youngest = 9 years old

2

^{nd}to the youngest = 9 + 4 = 13 2

^{nd}eldest = 9 = 4 = 13 2nd = 13 + 3 = 16

Eldest = 16 + 2 = 18

Ans: 1

16. Mary purchased 4 lbs. of mixed nuts at P20.00 per lb. Rita purchased 2 lbs of peanuts at P15.00 per lb. What is the average price per pound for the mixture of both purchases?

1. P18.33

2. P17.50

3. P20.00

4. P18.75

Solution: 4 lbs x P20 = P80.00

2 lbs x P15.00 =

__P30.00__ P110.00 / 6lbs = P18/lb.

Ans: 1

17. Mr. Vergara paid a total of P28,650 in taxes for income earned in s2006. His tax rate is 34 ¼ of his gross annual income. What is his monthly income?

1. P7,000

P6,970

P6,950

6,850

Solution: Tax paid = rate x annual gross income

tax rate = 34 ¼ % or .3425

p28.650 / .3425 = P83.650

Monthly salary : gross annual incoming /12 months

P83,650/12 = P 6,970

Ans: 2

18. On January 01, 2006. Margarita invested P100,000.00 ofr two years at a rate of 12% p.a compounded annually. By April 01, 2008, how much interest would she have earned?

1. P29,250.50

2. P29,203.20

3. P29,204.20

4. P29,205.50

5. P29,200.00

Solution: for 2006 : P 100,000 X 12% = p12,000 (yearly interest)

for 2007 : P112,000 x 12% = P13,440 (yearly interest)

for until April 01,2008 : P 125,440 x 12% = P15,052.80/12

P1,254.40(monthly interest) x23 months =

P3,363.20

Total interest earned : P12,000 + p13,440 + p3,763.20

P29,203.20

Ans: 2

19. On march 01, 2006.George opened a savings account of P50,000 at the rate of 6% per annum compound monthly. By June 01, 2006, how much is his money in the bank ?

1. P50,250

2. P50,753.75

3. P50,717.75

4. P50,500

Solution: annual interest : 6% ; monthly interest : ½ or .5%

by March 31 : (p50,000 x .005) + P50,000 = P50,250

by April 30 : (P50,250 x .005 ) + P52.250 = P50,501.25

BY May 31 : ( P50,501 .25x.005) + p50,501.25 = P50,753.75

Ans: 2

20. A Department store had a Megasale of Jackets at the ff. prices?

a. P395.00 jackets reduced to P300.00

b. P685.00 jackets reduced to p580.00

c. P995.00 jackets reduced to P890.00

d. P1,450.00 jackets reduced to P890.00

e.

which group of jackets was offered at the greatest rates of discounts from its original price?

a. 24%

b. 15%

c. 10%

d. 15%

e. 25%

SOLUTION: P395.00 – P300.00 = P95.00 difference

A. 95. 00 = .24% x 100% C.P995.00 – P 890.00 =

__P105.00__ 395.00 995.00

__95.00__=.10 x 100% = 10%

395.00

B. P685.00 – P580.00 = P 105.00/685.00 D. P1,450 – P1,250 =

__P200.00__ = .15 x 100% = 15% 1,450.00

=.13 x 100% = 13%