Time and Work

Original work = 6 x 30 x 9 = 1620 man-hours. Ten times that is 16200 man-hours. The new schedule gives 25 x 8 = 200 hours per man, so men needed = 16200 / 200 = 81, matching option C.

Let A take x days. Then B takes x/2 and C takes x/3. Combined rate: 1/x + 2/x + 3/x = 1/2. So 6/x = 1/2, which means x = 12. B's time is x/2 = 6 days. C's time would be 4 days. A's time is 12 days.

Regular hours: 5×8×4=160 hrs, pay=160×2.40=384. Remaining: 432-384=48. Overtime hours: 48÷3.20=15 hrs. Total: 160+15=175 hrs.

This is an inverse proportion: (Men1 * Days1) = (Men2 * Days2). 36 * 18 = 27 * Days2. Days2 = (36 * 18) / 27. Dividing 18 and 27 by 9 gives (36 * 2) / 3 = 12 * 2 = 24 days.

A's rate is 1/10 and B's rate is 1/12. Combined rate = 1/10 + 1/12 = (6+5)/60 = 11/60. The time taken together is the reciprocal: 60/11 = 5 5/11 days. Other options represent calculation errors in the common denominator or reciprocal.

Work rates: X=1/20, Y=1/30, Z=1/60 per day. First 4 days (all three): work done = 4*(1/20+1/30+1/60) = 4*(6/60) = 40/60. Next 6 days (X and Z): work done = 6*(1/20+1/60) = 6*(4/60) = 24/60. Total done = 64/60, but job is 60/60, so they overshot. Actually 4 days with all three + 6 days with X and Z = 10 days total. X alone needs to finish remaining work. Let me recalculate: first 4 days (X+Y+Z) = 4/10 = 2/5 work. Next 6 days (X+Z only) = 6*(1/20+1/60) = 6*(4/60) = 24/60 = 2/5. Total done = 4/5. Remaining = 1/5, which X does in (1/5)/(1/20) = 4 days.

Let Y's efficiency be 1 and wage be W. X's efficiency is 1.25 and wage is 1.25W. For the same work, X takes T/1.25 time. X's pay = (T/1.25) * 1.25W = TW = 75. Y's pay for the same work = T * W. Since TW = 75, Y also receives Rs.75.

Let m = one man's daily work, w = one woman's daily work. Then 4m + 6w = 1/8 and 3m + 7w = 1/10. Solving: multiply first by 3 (12m + 18w = 3/8), second by 4 (12m + 28w = 2/5). Subtract: 10w = 2/5 - 3/8 = 1/40. So 10 women complete 1/40 daily, taking 40 days total.

Total work = 18 × 4 × 8 = 576 man-hours. For 3× work = 1728 man-hours. Women efficiency = 0.5, so 12 women = 6 man-equivalent. Required days = 1728/(6 × 16) = 1728/96 = 18 days. Key insight: convert everything to equivalent man-hours and account for efficiency difference.

Anup's rate = 1/10 work per day, Jagdeesh's rate = 1/15. Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Time = 1/(1/6) = 6 days. This uses the standard work-rate formula.

Let total work be 360 units (LCM of 45 and 40). A's rate is 8 units/day, B's is 9 units/day. In the last 23 days, B did 23 * 9 = 207 units. The remaining 153 units (360 - 207) were done by A and B together. Their combined rate is 17 units/day. Thus, they worked together for 153 / 17 = 9 days.

This is an inverse proportion: (10 men * 4 days) = (8 men * x days). 40 = 8x, so x = 5. As the number of men decreases, the days required increase.

Work = Men × Days × Hours. Original work: 17 × 24 × 5 = 2040 man-hours. New work needed: 18 × Days × 4 = 2040. Days = 2040 / (18 × 4) = 2040 / 72 = 28.33 days. More men but fewer hours per day results in slightly fewer total days.

Let ‘W’ be the labour wages and ‘T’ be the working hours. Now, total cost is a function of W × T. Increase in wages = 20% $\therefore$ Revised wages = 1.2 W Decrease in labour time = $\left( \dfrac{100}{24}\% \right)$ $\therefore$Revised time = $\left( 1- \dfrac{1}{24}\right)T = \dfrac{23}{24}T$ $\therefore$Revised total cost = 1.2 $\times \dfrac{23}{24}$WT = 1.15 × WT                                     = 1.15 × 13200 = 15,180