6 goats or 8 sheeps can graze a field in 50 days. 8 goats and 6 sheeps can graze the field in: Option 1: 30 days Option 2: 16 days Option 3: 24 days Option 4: 32 days

Answer: 24 days. Solution: 6 goats can graze a field in 50 days, or 8 sheep can graze the same field in 50 days. Work done by 6 goats in 1 day = 1/50 Work done by 1 goat in 1 day = 1/50 6 = 1/300 Work done by 8 sheep in 1 day = 1/50 Work done by 1 sheep in 1 day = 1/50 8 = 1/400 Work done by 8 goats in 1 day = 8 x 1/300 = 8/300 = 2/75 Work done by 6 sheep in 1 day = 6 x 1/400 = 6/400 = 3/200 Total work done by 8 goats and 6 sheep in 1 day = 2/75 + 3/200 The LCM of 75 and 200 is 600. = 16/600 + 9/600 = 25/600 = 1/24 If 1/24 of the field is grazed in 1 day, then the entire field is grazed in 24 days. Therefore, 8 goats and 6 sheep can graze the field in 24 days.

Arithmetic

Time & Work

Medium

6 goats or 8 sheeps can graze a field in 50 days. 8 goats and 6 sheeps can graze the field in:

30 days

16 days

24 days

32 days

✅ Correct Option: 3

6 goats can graze a field in 50 days, or 8 sheep can graze the same field in 50 days.

Work done by 6 goats in 1 day $= \dfrac{1}{50}$

Work done by 1 goat in 1 day $= \dfrac{1}{50} \div 6$

$= \dfrac{1}{300}$

Work done by 8 sheep in 1 day $= \dfrac{1}{50}$

Work done by 1 sheep in 1 day $= \dfrac{1}{50} \div 8$

$= \dfrac{1}{400}$

Work done by 8 goats in 1 day $= 8 \times \dfrac{1}{300}$

$= \dfrac{8}{300}$

$= \dfrac{2}{75}$

Work done by 6 sheep in 1 day $= 6 \times \dfrac{1}{400}$

$= \dfrac{6}{400}$

$= \dfrac{3}{200}$

Total work done by 8 goats and 6 sheep in 1 day $= \dfrac{2}{75} + \dfrac{3}{200}$

The LCM of 75 and 200 is 600.

$= \dfrac{16}{600} + \dfrac{9}{600}$

$= \dfrac{25}{600}$

$= \dfrac{1}{24}$

If $\dfrac{1}{24}$ of the field is grazed in 1 day, then the entire field is grazed in 24 days.

Therefore, 8 goats and 6 sheep can graze the field in 24 days.

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6 goats or 8 sheeps can graze a field in 50 days. 8 goats and 6 sheeps can graze the field in:

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