Time and Work
- 2 men and 1 woman together can complete a piece of work in 14 days, while 4 women and 2 men together can do it in 8 days. If a man gets ₹ 600 per day, how much should a woman get per day?
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According to the question,
(2 × 14) men + 14 women = 16 men + 32 women
⇒ (28 – 16) men =(32–14) women
⇒ 12 men = 18 women
⇒ 2 men = 3 women∴ 1 woman = 2 man 3
∴ Amount received by 1 woman per day= 2 × 600 = ₹ 400 3 Correct Option: A
According to the question,
(2 × 14) men + 14 women = 16 men + 32 women
⇒ (28 – 16) men =(32–14) women
⇒ 12 men = 18 women
⇒ 2 men = 3 women∴ 1 woman = 2 man 3
∴ Amount received by 1 woman per day= 2 × 600 = ₹ 400 3
- If 6 persons working 8 hours a day earn ₹ 8400 per week, then 9 persons working 6 hours a day will earn per week
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More persons,
more earning
Direct proportion x Less working hours,
less earning∴ 6 : 9 : : 8400 : x 8 : 6
∴ 6 × 8 × x = 9 × 6 × 8400or x = 9 × 6 × 8400 = ₹ 9450 6 × 8
Aliter : Using Rule 1,
Here, M1 = 6, T1 = 8, wages = x
M2 = 9, T2 = 6, wages = 8400
6 × 8 × x = 9 × 6 × 8400x = 9 × 6 × 8400 = Rs 9450 6 × 8 Correct Option: C
More persons,
more earningDirect proportion x Less working hours,
less earning∴ 6 : 9 : : 8400 : x 8 : 6
∴ 6 × 8 × x = 9 × 6 × 8400or x = 9 × 6 × 8400 = ₹ 9450 6 × 8
Aliter : Using Rule 1,
Here, M1 = 6, T1 = 8, wages = x
M2 = 9, T2 = 6, wages = 8400
6 × 8 × x = 9 × 6 × 8400x = 9 × 6 × 8400 = Rs 9450 6 × 8
- A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for ₹ 3200. With the help of C they completed the work in 3 days. How much is to be paid to C ?
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Using Rule 25,
A’s 1 day’s work = 1 6 B’s 1 day’s work = 1 8 (A + B + C)’s 1 day’s work = 1 3
∴ C’s 1day’s work1 - 1 - 1 3 6 8 = 8 - 4 - 3 = 1 24 24
∴ Ratio of their one day’s work respectively1 : 1 : 1 = 4 : 3 : 1 6 8 24
Sum of the ratios = 4 + 3 + 1 = 8
∴ C’s share= ₹ 1 × 3200 = ₹ 400 8 Correct Option: B
Using Rule 25,
A’s 1 day’s work = 1 6 B’s 1 day’s work = 1 8 (A + B + C)’s 1 day’s work = 1 3
∴ C’s 1day’s work1 - 1 - 1 3 6 8 = 8 - 4 - 3 = 1 24 24
∴ Ratio of their one day’s work respectively1 : 1 : 1 = 4 : 3 : 1 6 8 24
Sum of the ratios = 4 + 3 + 1 = 8
∴ C’s share= ₹ 1 × 3200 = ₹ 400 8
- A and B can complete a piece of work in 15 days and 10 days respectively. They contracted to complete the work for ₹ 30,000. The share of A in the contracted money will be :
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A’s 1 day’s work = 1 15 B’s 1 day’s work = 1 10 Ratio = 1 : 1 = 2 : 3 15 10
Sum of the ratios = 2 + 3 = 5
∴ A’s share= ₹ 2 × 30000 = ₹ 12000 5
Aliter : Using Rule 24,
Here, m = 15, n = 10, R = 30,000Share of A = n × R m + n = 10 × 30000 15 + 10 = 10 × 30000 = ₹ 12,000 25 Correct Option: D
A’s 1 day’s work = 1 15 B’s 1 day’s work = 1 10 Ratio = 1 : 1 = 2 : 3 15 10
Sum of the ratios = 2 + 3 = 5
∴ A’s share= ₹ 2 × 30000 = ₹ 12000 5
Aliter : Using Rule 24,
Here, m = 15, n = 10, R = 30,000Share of A = n × R m + n = 10 × 30000 15 + 10 = 10 × 30000 = ₹ 12,000 25
- A man and a boy received ₹ 800 as wages for 5 days for the work they did together. The man’s efficiency in the work was three times that of the boy. What are the daily wages of the boy ?
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Man : boy = 3 : 1
∴ Boy's share = 1 × 800 = ₹ 200 4
∴ The daily wages of boy= ₹ 
200 
= ₹ 40 5
Aliter : Using Rule 16,
A:B = 3x:x and A:B = t:3tShare of boy = t × 800 = 200 t + 3t
Daily wages of boy= 200 = ₹ 40 5 Correct Option: D
Man : boy = 3 : 1
∴ Boy's share = 1 × 800 = ₹ 200 4
∴ The daily wages of boy= ₹ 200 = ₹ 40 5
Aliter : Using Rule 16,
A:B = 3x:x and A:B = t:3tShare of boy = t × 800 = 200 t + 3t
Daily wages of boy= 200 = ₹ 40 5
