連鎖規則 - 例題解析

題1 - 如果15個娃娃花費35盧比，那麼39個娃娃花費多少？

答案 - C

解釋

Let the required cost be Rs x.
More dolls, more cost  (direct)
∴ 15 : 39:: 35 : x ⇒15 *x = (39 *35)
⇒ x= (39 *35)/15 = 91.
∴  Cost of 39 dolls = Rs 91

題2 - 如果36個男人可以在25天內完成一件工作，那麼15個男人需要多少天才能完成？

答案 - D

解釋

Let the required number of days be x.
Less men, more days (indirect)
∴ 15: 36:: 25 : x ⇒ 15 *x = (36 * 25)
⇒ x= (36 *25 ) / 15 = 60.
∴ Required number of days = 60.

題3 - 如果20個男人可以在6天內建造112米長的牆，那麼25個男人在幾天內可以建造多長的一堵類似的牆？

答案 - D

解釋

Let the required length be x metres.
More men, more length built (direct)
Less days, less length built (direct)
Men 20 : 25 :: 112 : x  
Days 6:3           
∴ (20 * 6 *x ) =  ( 25 * 3 *112) ⇒ x= (25 * 3 * 112) / (20 * 6 ) = 70.
Required length 70m.

題4 - 如果8個男人每天工作9小時，可以在10天內建造一堵長18米、寬2米、高12米的牆，那麼需要多少個男人才能在8天內，每天工作6小時，建造一堵長32米、寬3米、高9米的牆？

答案 - A

解釋

let the required number of  men be x.
More length, more men   (Direct)
More breadth, more men    (Direct)
Less height, less men      (Direct)
Less hours per day, more men    (Indirect)
Less days, more men       (Indirect) 
Length       18:32
Breadth      2:3
Height       12:9 :: 8 : x
Hrs / Day    6: 9
Days         8:10
∴ ( 18 * 2 * 12 * 6 * 8 * x) = ( 32 * 3 * 9 * 9 * 10) ⇒ x= 32*3*9*9*10 / 
18*2*12*6*8 =30.

題5 - 一份合同要在56天內完成，並安排了104名工人，每人每天工作8小時。30天后，完成了2/5的工作。為了按時完成工作，可以額外僱傭多少人，每人現在每天工作9小時？

答案 - C

解釋

Remaining work = (1- 2/5 ) = 3/5 , Remaining period = (56 – 30) =26 days.
Let the additional men employed be x.
More work , more men   (direct)
More days , less men      (indirect)
More hrs/ day, less men    (indirect)
Work      2/5 : 3/5
Days       26: 30 :: 104 : (104 + x)
Hrs/ day    9:8
∴ 2/5 *26 * 9 * (104 +x ) = 3/5 *30 * 8 * 104
⇒ (104 +x) = 3 * 30 * 8 * 104 / 2* 26 * 9  = 160 ⇒ x = (160 – 104) = 56.
Additional men to be employed = 56.

題6 - 5個男人或9個女人可以在19天內完成一件工作。3個男人和6個女人需要多少天才能完成？

答案 - D

解釋

9 women = 5 men ⇒ 1 women = 5/9 men
⇒ 6 women = (5/9 * 6) men = 10/3 men.
3 men +6 women =  (3+ 10/3 ) men = 19/3 men.
Let the required number of days be x.
More men, less days
19/3 : 5 :: 19 : x ⇒ 19 /3 *x = (5 *19)
⇒ x= (5* 19 * 3 /19 ) = 15.
∴ Required number of days = 15.

題7 - 8個女人可以在10天內完成工作，10個孩子需要16天才能完成同樣的工作。10個女人和12個孩子需要多少天才能完成工作？

答案 - D

解釋

1 women can complete the work in (10 * 8) days= 80 days.
1 child can  complete the work in (16 * 10) days= 160 days.
1 women 1 days work = 1/80 , 1 child 1 days  work= 1/160.
(10 women +12 children) 1 days work = ( 10 * 1/80 +12 * 1/160)
=  ( 1/8 + 3/40 ) = 8/ 40  = 1 /5.
∴ 10 women and 12 children will finish the work in 5 days.

題8 - 如果6臺發動機每天執行9小時，消耗15公噸煤炭，那麼8臺發動機每天執行12小時需要多少煤炭，已知前一種型別的3臺發動機消耗的煤炭與後一種型別的4臺發動機一樣多？

答案 - D

解釋

Let the required quantity of coal consumed be x tones.
More engines, more coal consumption (direct)
More hours, more coal consumption     (direct)
Less rate of consumption, less consumption    (direct)
Engines      6:8
Working Hrs  9:12 :: 15 : x
Rate of consumption 1/3 : 1/4
∴ (6 * 9 * 1/3 * x) = (8 * 12 * 1/4 * 15 ⇒ 18x = 360 ⇒ x = 20.
Quantity of coal consumed = 20 tonnes.

題9 - 如果22.5米長的均勻鋼筋重85.5公斤，那麼6米長的相同鋼筋重多少？

答案 - A

解釋

Let the required weight be x kg.
Less length, less weight    (direct)
22.5: 6 :: 85.5 :x ⇒ 22.5x = (6 * 85.5) ⇒ x= (6 * 85.5) / 22.5 = (6 *885 / 225) = 22.8 kg.
Required weight = 22.8 kg.

題10 - 在地圖比例尺中，1.5釐米代表24公里。如果地圖上兩點之間的距離是76.5釐米，那麼這兩點之間的實際距離是多少？

答案 - B

解釋

Let the actual distance be x km.
More distance on the map, more is actual distance           (direct)
1.5 : 76.5 :: 24 : x ⇒ 1.5x = (76.5 * 24) ⇒ x = (76.5 * 24) / 1.5 = 1224 km.
Required  distance= 1224km.

題11 - 6打雞蛋花費48盧比。132個雞蛋要花費多少？

答案 - D

解釋

Let the required cost be Rs x. 
More eggs, more cost          ( direct)
72: 132 :: 48 : x ⇒ 72 x = (132 * 48) ⇒ x= (132 *48) / 72 = 88.
∴  Required  cost = Rs 88.

題12 - 在一場比賽中，拉古在20分鐘內跑了5公里，他在50分鐘內能跑多少距離？

答案 - A

解釋

Let the required distance be x km.
More time , more distance covered            ( direct)
20: 50: :: 5 : x ⇒ 20x = (50 * 5 ) ⇒ x= (50 * 5)  / 20 = 12.5 km.
Required   distance = 12.5 km.

aptitude_chain_rules.htm

列印頁面