连锁规则 - 例题解析

题1 - 如果15个娃娃花费35卢比，那么39个娃娃花费多少？

答案 - C

解释

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

题2 - 如果36个男人可以在25天内完成一件工作，那么15个男人需要多少天才能完成？

答案 - D

解释

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.

题3 - 如果20个男人可以在6天内建造112米长的墙，那么25个男人在几天内可以建造多长的一堵类似的墙？

答案 - D

解释

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.

题4 - 如果8个男人每天工作9小时，可以在10天内建造一堵长18米、宽2米、高12米的墙，那么需要多少个男人才能在8天内，每天工作6小时，建造一堵长32米、宽3米、高9米的墙？

答案 - A

解释

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.

题5 - 一份合同要在56天内完成，并安排了104名工人，每人每天工作8小时。30天后，完成了2/5的工作。为了按时完成工作，可以额外雇佣多少人，每人现在每天工作9小时？

答案 - C

解释

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.

题6 - 5个男人或9个女人可以在19天内完成一件工作。3个男人和6个女人需要多少天才能完成？

答案 - D

解释

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.

题7 - 8个女人可以在10天内完成工作，10个孩子需要16天才能完成同样的工作。10个女人和12个孩子需要多少天才能完成工作？

答案 - D

解释

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.

题8 - 如果6台发动机每天运行9小时，消耗15公吨煤炭，那么8台发动机每天运行12小时需要多少煤炭，已知前一种类型的3台发动机消耗的煤炭与后一种类型的4台发动机一样多？

答案 - D

解释

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.

题9 - 如果22.5米长的均匀钢筋重85.5公斤，那么6米长的相同钢筋重多少？

答案 - A

解释

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.

题10 - 在地图比例尺中，1.5厘米代表24公里。如果地图上两点之间的距离是76.5厘米，那么这两点之间的实际距离是多少？

答案 - B

解释

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.

题11 - 6打鸡蛋花费48卢比。132个鸡蛋要花费多少？

答案 - D

解释

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.

题12 - 在一场比赛中，拉古在20分钟内跑了5公里，他在50分钟内能跑多少距离？

答案 - A

解释

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.

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