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R 13 Veto follow us: facebook.com/vetotrivandrum 14 Work and Time type - i 1. A can do a work in 6 days B can do the some work in 3 days. In howmany days working together they will finish the same work? (a) 3 days (b) 9 days (c) 2 days (d) None Ans: (c) 2 days A can do a work in x days B can do the same work in y days then A and B can do the work in xy x+ y OR days A→ x days B→ y days A+B = Exp: x = 6 y = 3 6× 3 6× 3 = = 2days 6+ 3 9 2. A and B can seperately finish a work in 10 days and 15 days respectively. In how may days working together, they will finish the work? (a) 6 days (c) 9 days xy x+ y Ans: (a) 6 days (b) 2 days (d) 3 days Exp: x = 10, y = 15 xy 10× 15 10× 15 = = = 6 days x+ y 10 + 15 25 type - iI 3. A can do a work in 30 days. B can do the same work in 60 days. C can do the same work in 80 days. A, B and C working together, in how many days they will finish the same work? (a) 9 days (b) 16 days (c) 10 days (d) None of these Ans: (b) 16 days hnPbIpamÀ imkvXmwtIm« A→ x days B → y days C → z days ü A+B+C = days xy + yz + xz Exp: x = 30, y = 60, z = 80 xyz xy + yz + xz 30× 60× 80 = 30× 60 + 60× 80 + 30× 80 30× 60× 80 = 1800 + 4800 + 2400 30× 60× 80 = = 16 days 9000 4. A, B and C can do a work seperately in 10 days, 15 ays and 30 days. In how many days working together they will finish the work? (a) 6 days (c) 4 days Ans: (b) 5 days (b) 5 days (d) 2 days Exp: x = 10, y = 15, z = 30 xyz = xy + yz + xz 10× 15× 30 = 10× 15 + 15× 30 + 10× 30 10× 15× 30 = 150 + 450 + 300 10× 15× 30 = = 5 days 900 type - iII 5. A and B together can complete a work in 12 days. If A alone can finish the same work in 18 days. In how many days B alone can finish the same work? (a) 18 days (b) 36 days (c) 72 days (d) None of these Ans: (b) 36 days A+B→ x days A → y days B→ xy y− x days Exp: x = 12, y = 18 xy y x 12× 18 12× 18 = = = 36 days 18 12 6 6. A and B and C together can complete a work in 10 days. If B and C together alone can complete the same work in 15 days. In how many days A alone can complete the same work? (a) 15 days (c) 25 days Ans: (b) 30 days (b) 30 days (d) None of these Exp: x = 10, y = 15 xy y x 10× 15 10× 15 = = = 30 days 15 10 5 type - iV 7. If 12 men can do a job in 16 days. In how many days 8 men can complete the work? (a) 12 days (b) 24 days (c) 30 days (d) None of these Ans: (b) 24 days 12m →16days Exp : 8 m → ? 12× 16 = = 24 days 8 Short Cut Numerator = Multiply the 1 st row Denominator = 2 nd row 8. 21 men can do a job in 10 days. In how many men can do finish the same work in 7 days? (a) 20 (b) 30 (c) 15 (d) None of these Ans: (b) 30 21m →10days Exp : ? → 7days 21× 10 = = 30 men 7 9. In a camp, there are 50 days food in 20 peoples. If 5 more peoples attend the camp. In how many days food are sufficient in the camp? (a) 30 days (c) 40 days Ans: (b) 30 (b) 25 days (d) None of these 5 more people attend the camp ∴Total people = 20 + 5 = 25 20 → 50days ü → 20× 50 Exp : = 40 days 25 type - V 10. 6 men or 8 women can do a job in 46 days. How long will 8 men and 20 women do the same job? (a) 10 days (b) 12 days (c) 6 days (d) None of these Ans: (b) 12 days 6m or 8w → 46 days 8m and 20 w → ? No. of days (or/and) 6× 8× 46 6× 8× 46 = = 6× 20 + 8× 8 120 + 64 6× 8× 46 = = 12 days 184 Short-cut Multiply the 1st row (Numerator) Cross xied and added each other (denominator) 11. 3 men or 4 women can do a job in 43 days. How long will 7 men and 5 women do the same job? (a) 12 days (b) 24 days (c) 48 days (d) 6 days Ans: (a) 12 days 3m or 4w → 43 days = 7m and 5 w → ? 3× 4× 43 3× 4× 43 Exp : = = = 12 days 15 + 28 43 12. 8 men or 12 women can do a job in 18 days. How long will 18 men and 9 women do the same job? (a) 3 days (b) 6 days (c) 12 days (d) None of these Ans: (b) 6 days 8m or 12w →18 days 18m and 9 w → ? 8× 12× 18 8× 12× 18 Exp : ℵ 72 + 216 288 type - VI 6days 13. 1 men or 2 women or 3 boys do a piece of job in 44 days. In howmany days to finish the same piece of job done by 1 men and 1 women and 1 boy? (a) 44 days (b) 24 days (c) 22 days (d) 12 days Ans: (b) 24 days 1M or 2W or 3B → 44days Exp : 1M and 1W and 1B → ?
R 13 Veto follow us: facebook.com/vetotrivandrum 15 No. of days (or/or and/and 1,1,1(2 nd row) No. of days (or/or and/and 1× 2× 3× 44 = 1 × 2 + 2 × 3 + 1 × 3 1× 2× 3× 44 = 2+ 6+ 3 1× 2× 3× 44 = = 24 days 11 Short-cut Nr: Multiply the 1 st row Dr: Multiply each 2 category member’s of the group in the 1 st row 14. 2 men or 3 women or 4 boys do a job in 52 days. In how many days 1 men and 1 women and 1 boy do the same job? (a) 24 days (b) 48 days (c) 12 days (d) 16 days Ans: (b) 48 days Exp: 2M or 3W or 4B →52 days 1M and 1W and 1B →? 2× 3× 4× 52 2× 3× 4× 52 = 2× 3+ 3× 4+ 2× 4 6+ 12+ 8 2× 3× 4× 52 = = 48 days 26 type - VII 15. 2 men or 4 women or 8 children do a job in 10 days. In how many days 1 men and 1 women and 2 children do the same job? (a) 11 days (c) 9 days Ans: (b) 10 days (b) 10 days (d) 8 days Exp: 2M or 4W or 8C →10 days 1M and 1W and 2C →? Nr: 2 nd row Dr: 1 st row ⎛1 1 2⎞ 1 ⎛1 1 1⎞ 1 = ⎜ + + ⎟× = ⎜ + + ⎟× ⎝2 4 8⎠ 10 ⎝2 4 4⎠ 10 ⎛1 2⎞ 1 ⎛1 1⎞ 1 = ⎜ + ⎟× = ⎜ + ⎟× ⎝2 4 ⎠ 10 ⎝2 2 ⎠ 10 1 1 = 1× = =10 days 10 10 Short-cut each 2 nd row by 1 st row and adding 16. 2 men or 4 women or 6 boy do a job in 49 days. In how many days can finish the same work by 3 men and 5 women and 8 boy? (a) 6 days (b) 12 days (c) 10 days (d) 8 days Ans: (b) 12 days Exp: 2M or 4W or 6B→49 days 3M and 5W and 8B →? ⎛3 5 8⎞ 1 ⎜ + + ⎟× ⎝2 4 6 ⎠ 49 LCM of 2,4,6 ü 12× 2,4,6 ü + 12× + 12× 1 × 1,2,3 12 12 49 18 + 15 + 16 1 49 1 1 × = × = 12 49 12 49 12 = 12 days type - VIII 17. A can do a work in 30 days. B can the same work in 25 days. B worked in 10 days and left the job. In how many days A alone can finish the remaining work? (a) 15 days (b) 18 days (c) 21 days (d) 20 days Ans: (b) 18 days Exp: A B 30(p) 25(q) 10(r) q− r No. of days = × p q p - single, q and r - pairs 25 −10 15 left the job = × 30 = × 30 25 25 = 18 days 18. A can do a work in 30 days. B can the same work in 45 days. ‘A’ worked in 12 days and left the job. In how many days B alone can finish the remaining work? (a) 25 days (b) 27 days (c) 30 days (d) 35 days Ans: (b) 27 days Exp: A B 30(p) 45(q) 12(r) q− r No. of days = × p q 30 −12 18 = × 45 = × 45 30 30 = 27 days type - IX 19. 4 men can do a work in 5 days and 6 women can dot he same work in 4 days. If 5 men and 6 women work together, they will complete the work in how many days? (a) 1 days (c) 3 days Ans: (b) 2 days Exp: (b) 2 days (d) 4 days 4 M →5 days 6 W →4 days 5 M→? 6 W →? 4× 5 5 M = = 4 days 5 6× 4 6 W = = 4 days 6 x= 4, y = 4 xy 4× 4 16 5M + 6W = = = = 2 x+ y 4+ 4 2 = days 20. 3 men can do a work in 4 days and 4 women can do a work in 6 days. If 3M and 6W work together, they will complete the work in how many days? (a) 1 days (b) 2 days (c) 3 days (d) 4 days Ans: (b) 2 days Exp: 3 M →4 days 4 W →6 days 3 M →? 6 W → ? 3× 4 3 M = = 4 days 3 4× 6 6 W = = 4 days 6 a = 4, b = 4 ab 4× 4 4× 4 16 3M + 6W = = = = = 2 days a + b 4+ 4 8 8 type - X 21. A is twice as good a workman as B. They together finish a piece of work in 14 days A alone can finish the work in how many days? (a) 20 days (b) 21 days (c) 24 days (d) 30 days Ans: (b) 21 days Exp: A:B = 2:1 1 A + B = 14 As ' A’s alone work= Total × Total 1 2 1 A’s alone day = × = 14 3 21 = 21 day 22. B is thrice as good a workman as A. They together finish a piece of job in 6 days. In how many day, B alone can finish the work? (a) 6 days (b) 8 days (c) 10 days (d) 12 days Ans: (b) 8 days Exp: A:B = 1 1:3 A + B = 6 ü B = = 8 days 3 (1) x 3 →2 M + 18 W = ........ (3) 8 4 (2) x 4 →12 M + 218 W = ..... (4) 10 4 3 4 - 3 →10 M = − 10 8 2 3 2 3 − = × 40 − × 40 5 8 5 8 16 −15 1 = = = 40 40 40 = 40 days 24. 5 M and 8W can finish a job in 10 days. While 3M and 7W can finish it in 12 days. In how many days can 11 men to finish it? (a) 30 days (c) 20 days (b) 10 days (d) 12 days Ans: (a) 30 days 1 Exp: 5M + 8W = ........ (1) 10 3M + 7W = ........ (2) (1) x 7→35 M + 56 W 7 = ................ (3) 10 (2) x 8 →24 M + 56 8 W = 12 ................ (4) 7 8 (4) - (3) → 11 M = − 10 12 7 2 7 2 30× 10 − 30× 3 = − = 10 3 30 21− 20 1 = = 30 30 = 30 days 1 12 U-19 {In¡äv temI-I¸v Cýbv¡v 4þmw IncoSw ü × = $ ss^\-enÂ Hmkvt{S-en-bsb type - XI ]cm-P-b-s¸-Sp¯n $ am³ Hm^v Zn am¨v þ a³tPmXv 23. 4 M and 6W finish a job in 8 days. While 3 M and 7W finish it in 10 $ am³ Hm^v Zn SqÀW-saâ v days. In how many days 10 W þ ip`v am³ KnÂ can finish the job? $ Cý³ Soansâ ]cn-io-e-I-\m-bncp-Xv þ cmlpÂ {ZmhnUv (a) 30 days (b) 40 days $ thZn-bmb cmPyw þ \yqkvemâ v (c) 24 days (d) 20 days $ thÄUv I¸v Cý³ Soans\ Ans: (b) 40 days \bn-¨Xv þ ]rYzn jm 1 Exp: 4M + 6W = 8 ........ (1) $ 2020 se thÄUv I¸v thZn 1 þ ku¯v B{^n¡ 3M + 7W = 10 ............. (2) $ 2022 se thZn þ shÌv C³Uokv
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