Piecework
A worker earns ₱48.00 for every acceptable item produced. Out of 35 items, 4 fail the quality inspection. How much does the worker earn?
Acceptable items = 35 - 4 = 31
Earnings = 31(₱48) = ₱1,488
Answer: ₱1,488.00
A salesperson earns a 3.5% commission on ₱280,000.00 in valid sales. How much commission does the salesperson earn?
Commission = ₱280,000(0.035) = ₱9,800
Answer: ₱9,800.00
An employee earns ₱120.00 per hour and works 3 overtime hours on an ordinary workday. How much is the overtime pay?
OT pay = ₱120(3)(1.25) = ₱450
Answer: ₱450.00
An employee earns ₱1,000.00 per day and works exactly 8 hours on a special non-working day. How much does the employee earn?
Pay = ₱1,000(1.30) = ₱1,300
Answer: ₱1,300.00
The sum of four consecutive integers is 106. What is the largest integer?
Let the integers be n, n + 1, n + 2, and n + 3.
n + (n + 1) + (n + 2) + (n + 3) = 106
4n + 6 = 106
4n = 100
n = 25
The integers are 25, 26, 27, and 28.
Answer: 28
A piecework worker earns ₱55.00 per acceptable unit. The employer guarantees a minimum daily wage of ₱720.00. If the worker completes 12 acceptable units, how much will the worker receive?
Piecework earnings = 12(₱55) = ₱660
Since ₱660 is below the guaranteed minimum of ₱720, the worker receives the guaranteed amount.
Answer: ₱720.00
A salesperson earns a monthly salary of ₱22,000.00 plus a 2.5% commission on ₱640,000.00 in sales. What is the salesperson’s total gross income?
Commission = ₱640,000(0.025) = ₱16,000
Total gross income = ₱22,000 + ₱16,000 = ₱38,000
Answer: ₱38,000.00
An employee earns ₱960.00 per day and works for 11 hours on an ordinary workday. What is the employee’s total gross pay?
Hourly rate = ₱960 ÷ 8 = ₱120
Overtime hours = 11 - 8 = 3
Overtime pay = ₱120(3)(1.25) = ₱450
Total gross pay = ₱960 + ₱450 = ₱1,410
Answer: ₱1,410.00
An employee earns ₱1,200.00 per day and receives ₱1,800.00 for exactly 8 hours of work. What type of day was it?
Multiplier = ₱1,800 ÷ ₱1,200 = 1.50
A 1.50 multiplier applies to a special non-working day that falls on the employee’s scheduled rest day.
Answer: A special non-working day that fell on the employee’s rest day
A two-digit number is 27 greater than the number formed by reversing its digits. The sum of its digits is 11. What is the original number?
Let t be the tens digit and u be the units digit.
t + u = 11
(10t + u) - (10u + t) = 27
9t - 9u = 27
t - u = 3
Solving t + u = 11 and t - u = 3 gives t = 7 and u = 4.
Answer: 74
A worker earns ₱42.00 per acceptable item. On a regular holiday, the worker produces 30 acceptable items during an 8-hour shift. How much is the worker’s total pay?
Base piecework earnings = 30(₱42) = ₱1,260
Regular-holiday pay = ₱1,260(2) = ₱2,520
Answer: ₱2,520.00
A salesperson earns a 2% commission on the first ₱500,000.00 in sales and 4% on the amount exceeding ₱500,000.00. If total sales are ₱1,100,000.00, how much commission does the salesperson earn?
First tier = ₱500,000(0.02) = ₱10,000
Amount exceeding ₱500,000 = ₱1,100,000 - ₱500,000 = ₱600,000
Second tier = ₱600,000(0.04) = ₱24,000
Total commission = ₱10,000 + ₱24,000 = ₱34,000
Answer: ₱34,000.00
An employee earns ₱125.00 per hour and receives ₱1,625.00 for an ordinary workday. How many overtime hours did the employee render?
Pay for the first 8 hours = ₱125(8) = ₱1,000
Overtime pay = ₱1,625 - ₱1,000 = ₱625
Overtime rate = ₱125(1.25) = ₱156.25
Overtime hours = ₱625 ÷ ₱156.25 = 4
Answer: 4 overtime hours
An employee earns ₱1,100.00 per day and receives ₱2,860.00 for exactly 8 hours of work. What type of day was it?
Multiplier = ₱2,860 ÷ ₱1,100 = 2.60
A 2.60 multiplier applies to a regular holiday that falls on a scheduled rest day.
Answer: A regular holiday that fell on the employee’s rest day
The product of two positive integers is 180, and their greatest common divisor is 6. What is the least possible value of their sum?
Let the integers be 6a and 6b, where gcd(a, b) = 1.
(6a)(6b) = 180
36ab = 180
ab = 5
The only positive coprime factor pair is 1 and 5.
The integers are 6 and 30.
Their sum is 6 + 30 = 36.
Answer: 36
A piecework employee earns ₱50.00 per acceptable item. On a regular holiday, the employee works for 10 hours and produces 28 acceptable items. What is the employee’s total gross pay?
Base piecework earnings = 28(₱50) = ₱1,400
Pay for the first 8 hours = ₱1,400(2) = ₱2,800
Equivalent hourly rate = ₱1,400 ÷ 8 = ₱175
Overtime pay = ₱175(2)(2.60) = ₱910
Total gross pay = ₱2,800 + ₱910 = ₱3,710
Answer: ₱3,710.00
A salesperson earns a salary of ₱25,000.00 and receives a 3% commission on valid sales exceeding ₱700,000.00. If the salesperson’s total gross income is ₱43,000.00, what were the total valid sales?
Commission earned = ₱43,000 - ₱25,000 = ₱18,000
Sales subject to commission = ₱18,000 ÷ 0.03 = ₱600,000
Total valid sales = ₱700,000 + ₱600,000 = ₱1,300,000
Answer: ₱1,300,000.00
An employee earns ₱150.00 per hour and works for 10 hours on a scheduled rest day. What is the employee’s total gross pay?
Pay for the first 8 hours = ₱150(8)(1.30) = ₱1,560
Overtime pay = ₱150(2)(1.30)(1.30) = ₱507
Total gross pay = ₱1,560 + ₱507 = ₱2,067
Answer: ₱2,067.00
An employee earns ₱1,200.00 per day and works for 10 hours on a regular holiday. What is the employee’s total gross pay?
Hourly rate = ₱1,200 ÷ 8 = ₱150
Pay for the first 8 hours = ₱1,200(2) = ₱2,400
Overtime pay = ₱150(2)(2)(1.25) = ₱750
Total gross pay = ₱2,400 + ₱750 = ₱3,150
Answer: ₱3,150.00
A positive integer leaves a remainder of 2 when divided by 5, a remainder of 3 when divided by 7, and a remainder of 4 when divided by 9. What is the smallest possible integer?
Numbers satisfying the first two conditions include 17, 52, 87, 122, 157, ...
157 ÷ 9 leaves a remainder of 4.
Therefore, 157 satisfies all three conditions.
Answer: 157
A piecework employee earns ₱36.00 per acceptable item. On a regular holiday, the employee works for 11 hours and receives total gross earnings of ₱3,384.00. How many acceptable items did the employee produce?
Let n be the number of acceptable items.
Base piecework earnings = ₱36n
Pay for the first 8 hours = ₱36n(2) = ₱72n
Equivalent hourly rate = ₱36n ÷ 8 = ₱4.50n
Overtime pay = ₱4.50n(3)(2.60) = ₱35.10n
₱72n + ₱35.10n = ₱3,427.20
₱107.10n = ₱3,427.20
n = 32
A salesperson earns a 1.5% commission on the first ₱800,000.00, 3% on the next ₱700,000.00, and 5% on sales exceeding ₱1,500,000.00. If the total commission is ₱58,000.00, what is the total sales amount?
First tier = ₱800,000(0.015) = ₱12,000
Second tier = ₱700,000(0.03) = ₱21,000
Commission from the first two tiers = ₱33,000
Commission from final tier = ₱58,000 - ₱33,000 = ₱25,000
Sales above ₱1,500,000 = ₱25,000 ÷ 0.05 = ₱500,000
Total sales = ₱1,500,000 + ₱500,000 = ₱2,000,000
Answer: ₱2,000,000.00
An employee earns ₱1,400.00 per day and receives ₱4,823.00 after working on a regular holiday that fell on a scheduled rest day. How many overtime hours did the employee render?
Hourly rate = ₱1,400 ÷ 8 = ₱175
Pay for the first 8 hours = ₱1,400(2.60) = ₱3,640
Overtime pay = ₱4,823 - ₱3,640 = ₱1,183
Overtime rate = ₱175(2.60)(1.30) = ₱591.50
Overtime hours = ₱1,183 ÷ ₱591.50 = 2
Answer: 2 overtime hours
An employee earns ₱125.00 per hour and works for 10 hours on a special non-working day that falls on a scheduled rest day. Four of the first 8 hours and both overtime hours fall within the Night Shift Differential period. What is the employee’s total gross pay?
Pay for the first 8 hours = ₱125(8)(1.50) = ₱1,500
Overtime pay = ₱125(2)(1.50)(1.30) = ₱487.50
NSD for 4 regular hours = ₱125(1.50)(0.10)(4) = ₱75
NSD for 2 overtime hours = ₱125(1.50)(1.30)(0.10)(2) = ₱48.75
Total gross pay = ₱1,500 + ₱487.50 + ₱75 + ₱48.75 = ₱2,111.25
Answer: ₱2,111.25
A three-digit number is divisible by 9. When its digits are reversed, the new number is 198 less than the original number. The hundreds digit is twice the units digit. What is the original number?
432