Class 10 Work Rates with Two Unknowns — practice questions with answers

Algebra — Systems of Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. 2 women and 5 men finish a piece of embroidery in 4 days; 3 women and 6 men finish it in 3 days. How long would one woman take alone?

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Answer: D) 18 days

Let a woman do

u

and a man

v

per day:

2 u + 5 v = \frac{1}{4}

3 u + 6 v = \frac{1}{3}

. Solving,

u = \frac{1}{18}

v = \frac{1}{36}

2. 5 men and 2 boys finish a job in 5 days, and so do 4 men and 4 boys. How long would one boy take alone?

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Answer: C) 60 days

m = 2 b

5 (2 b) + 2 b = 12 b = \frac{1}{5}

, so

b = \frac{1}{60}

3. With 3a + 2b = 360 and 2a + 3b = 340 (units per hour of two machines), what is b?

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Answer: A) 60 units

a + b = 140

and

a - b = 20

give

b = 60

4. A and B can do a job together in 15 days. After 6 days together, A leaves and B finishes in 18 more days. How long would A take alone?

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Answer: A) 30 days

a = \frac{1}{15} - \frac{1}{30} = \frac{1}{30}

: 30 days. They happen to be equally fast.

5. 2 pumps of type A and 1 of type B empty a tank in 4 hours; 1 of type A and 3 of type B take 4 hours too. How many B pumps equal one A pump?

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Answer: B) 2

Same time, so

2 a + b = a + 3 b

a = 2 b

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