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2 men and 3 boys together can do a piece of workin 8 days. The same work is done in 6 days by3 men and 2 boys together. How long would 1 boyalone and 1 man alone take to complete the workindependently?(1) 40 days, 120 days(2) 120 days, 40 days(3) 20 days, 120 days(4) 120 days, 20 days |
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Answer» Answer: 20 DAY, 120 days Step-by-step explanation: Let the no. of days taken by men be 'x' and thatby boys be 'y'. According to the conditions given, the eq can be written as FOLLOWS... 2/x + 3/y = 1/8. 3/x +2/y = 1/6. Substitute 1/x = a and 1/y = b therefore, 2a+3b = 1/8. ... (1) 3a+4b = 1/6. ....(2) Since we NEED the denominator as 1 So multiply eq. 1 by 8 and eq. 2 by 6 this way we get the following eqs. 16a + 24b = 1. ...(3) 18a + 12b = 1. ...(4) Subtract eq.3 and 4, 16a + 24b = 1 - 18a + 12b = 1 -2a +12b = 0 2a = 12b a = 6b. ...(5) Substitute eq. 5 in eq.3 16(6b) + 24b = 1 96b + 24b = 1 120b = 1 b = 1/120 substitute the VALUE of b in eq. 4 18a + 12 × 1 /120 = 1 18a + 1 / 10 = 1 18a = 1 - 1/ 10 18a = 9/10 a = 9/10 × 1/18 a = 1/10 × 1/2 a = 1/20 Let's replace the VALUES of a and b a = 1/20 = 1/x therefore, x = 20 b = 1/120 = 1/y therefore, y = 120. |
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