Time and Work
- Koushik can do a piece of work in x days and Krishnu can do the same work in y days. If they work together, then they can do the work in
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Koushik’s 1 day’s work
= 1 x Krishnu’s 1 day’s work = 1 y
∴ One day’s work of both= 1 + 1 = x + y x y xy ∴ Required time = xy days x + y Correct Option: C
Koushik’s 1 day’s work
= 1 x Krishnu’s 1 day’s work = 1 y
∴ One day’s work of both= 1 + 1 = x + y x y xy ∴ Required time = xy days x + y
- A and B together can do a piece of work in 36 days, B and C together can do it in 24 days. A and C together can do it in 18 days. The three working together can finish the work in
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(A + B)’s 1 day’s work = 1 36 (B + C)’s 1 day’s work = 1 24 (A + C)’s 1 day’s work = 1 18
On adding all three,
2 (A + B + C)’s 1 day’s work= 1 + 1 + 1 36 24 18 = 2 + 3 + 4 72 = 9 = 1 72 8
∴ (A + B + C)’s 1 day’s work= 1 16
∴ Required time = 16 daysCorrect Option: B
(A + B)’s 1 day’s work = 1 36 (B + C)’s 1 day’s work = 1 24 (A + C)’s 1 day’s work = 1 18
On adding all three,
2 (A + B + C)’s 1 day’s work= 1 + 1 + 1 36 24 18 = 2 + 3 + 4 72 = 9 = 1 72 8
∴ (A + B + C)’s 1 day’s work= 1 16
∴ Required time = 16 days
- If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?
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10 men ≡ 20 boys
∴ 1 man ≡ 2 boys
∴ 8 men + 4 boys
= (16 + 4) boys = 20 boys
Hence, 8 men and 4 boys will make 260 mats in 20 days.Correct Option: A
10 men ≡ 20 boys
∴ 1 man ≡ 2 boys
∴ 8 men + 4 boys
= (16 + 4) boys = 20 boys
Hence, 8 men and 4 boys will make 260 mats in 20 days.
- 3 men and 4 boys can complete a piece of work in 12 days. 4 men and 3 boys can do the same work in 10 days. Then 2 men and 3 boys can finish the work in number of days is
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12 (3 men + 4 boys)
= 10 (4 men + 3 boys)
⇒ 36 men + 48 boys
= 40 men + 30 boys
⇒ 4 men = 18 boys
or 2 men = 9 boys
∴ 4 men + 3 boys
= 21 boys who do the work in 10 days and, 2 men + 3 boys = 12 boys
∴ M1D1 = M2D2
⇒ 21 × 10 = 12 × D2⇒ D2 = 21 × 10 = 35 = 17 1 days 12 2 2
Aliter :
Using Rule 11,
Here, A1 = 3, B1 = 4, D1 = 12
A2 = 4, B2 = 3, D2 = 10
A3 = 2, B3 = 3Required time = D1D2(A1B2 - A2B1) days D1(A1B3 - A3B1) - D2(A2B3 - A3B2) = 12 × 10(3 × 3 - 4 × 4) days 12(3 × 2 - 2 × 4) - 10(4 × 3 - 2 × 3) = - 120 × 7 = - 840 = 70 = 35 = 17 1 days 12 - 60 - 48 4 2 2 Correct Option: A
12 (3 men + 4 boys)
= 10 (4 men + 3 boys)
⇒ 36 men + 48 boys
= 40 men + 30 boys
⇒ 4 men = 18 boys
or 2 men = 9 boys
∴ 4 men + 3 boys
= 21 boys who do the work in 10 days and, 2 men + 3 boys = 12 boys
∴ M1D1 = M2D2
⇒ 21 × 10 = 12 × D2⇒ D2 = 21 × 10 = 35 = 17 1 days 12 2 2
Aliter :
Using Rule 11,
Here, A1 = 3, B1 = 4, D1 = 12
A2 = 4, B2 = 3, D2 = 10
A3 = 2, B3 = 3Required time = D1D2(A1B2 - A2B1) days D1(A1B3 - A3B1) - D2(A2B3 - A3B2) = 12 × 10(3 × 3 - 4 × 4) days 12(3 × 2 - 2 × 4) - 10(4 × 3 - 2 × 3) = - 120 × 7 = - 840 = 70 = 35 = 17 1 days 12 - 60 - 48 4 2 2
- 2 men and 3 women can do a piece of work in 10 days while 3 men and 2 women can do the same work in 8 days. Then, 2 men and 1 woman can do the same work in
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2 × 10 men + 3 × 10 women
= 3 × 8 men + 2 × 8 women
⇒ 20 men + 30 women = 24 men + 16 women
⇒ 4 men = 14 women or 2 men = 7 women
∴ 2 men + 3 women = 10 women
∴ 2 men + 1 woman = 8 women
∴ M1D1 = M2D2
⇒ 10 × 10 = 8 × D2⇒ D2 = 25 = 12 1 days 2 2
Aliter :
22 (Using Rule 11),
Here, A1 = 2, B1 = 3, D1 = 10
A2 = 3, B2 = 2, D2 = 8
A3 = 2, B3 = 1Required time = D1D2(A1B2 - A2B1) days D1(A1B3 - A3B1) - D2(A2B3 - A3B2) = 10 × 8(2 × 2 - 3 × 3) days 10(2 × 1 - 2 × 3) - 8(3 × 1 - 2 × 2) = 10(2 × 4 - 9) days 10(2 - 6) - 8(3 - 4) = - 400 = 25 - 32 2 = 12 1 days 2 Correct Option: B
2 × 10 men + 3 × 10 women
= 3 × 8 men + 2 × 8 women
⇒ 20 men + 30 women = 24 men + 16 women
⇒ 4 men = 14 women or 2 men = 7 women
∴ 2 men + 3 women = 10 women
∴ 2 men + 1 woman = 8 women
∴ M1D1 = M2D2
⇒ 10 × 10 = 8 × D2⇒ D2 = 25 = 12 1 days 2 2
Aliter :
22 (Using Rule 11),
Here, A1 = 2, B1 = 3, D1 = 10
A2 = 3, B2 = 2, D2 = 8
A3 = 2, B3 = 1Required time = D1D2(A1B2 - A2B1) days D1(A1B3 - A3B1) - D2(A2B3 - A3B2) = 10 × 8(2 × 2 - 3 × 3) days 10(2 × 1 - 2 × 3) - 8(3 × 1 - 2 × 2) = 10(2 × 4 - 9) days 10(2 - 6) - 8(3 - 4) = - 400 = 25 - 32 2 = 12 1 days 2
