#1 Bucket pakhat leh tui herh haw na(water-tap) pathum i nei a. Water-tap tê ber chuan minute 20 chhungin baket chu a ti khat theia, water-tap laihawl(middle) chuan minute 12 chhungin, water-tap lian ber chuan minute 5 chhungin.
Q. water-tap zawng zawng ṭangrual hian minute engzat ah nge bucket hi an tih khah theih ang?
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#2 Lehkhabu pakhat ah hian phek engemaw zat chu a indawt(consecutive pages) in a kim lova. Chung phek kim lo ho page number ṭheuh te belhkhawm chu 9808 a ni.
Q. A bo chin chu phek engzatna aṭanga engzatna nge? Phek no 1 leh no 9808 hman awihloh.
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PS: A pahnih a chhang dik (Justify na telin) in awm chuan ka lo mail che u anga in account no. min pe ang a, chuan lawmman ah cheng 100 ka lo thun ang che u OR in phone balance ah. 
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(Y)
December 8th, 2011 at 8:32 pm
Hmmm… a hma ai chuan a har deuh…
Answer 1
Hei hi bucket size (volume) i pe si lova, a chhut theihloh ka rawn ti tep a, mahse heti hian ka chhut ve leh chhin a, ka dik a ngem aw?
Bucket tih full nan:
smallest watertap [A] = 20 minutes
medium watertap [B] = 12 minutes
largest water tap [C] = 5 minute
Chuvangin
[A] chuan minute khatah bucket 1/20 a fill thei
[B] chuan minute khatah bucket 1/12 a fill thei
[C] chuan minute khatah bucket 1/5 a fill thei
A, B leh C a rual a hawng chuan, minute khatah bucket heti zat hi an fill thei
1/20 + 1/12 + 1/5 = 20/60 = 1/3
Minute khat chhung chuan bucket 1/3 (hmun thuma hmun khat) a khat
Chuvangin minute hnih chuan bucket 2/3 a khat
Minute thum chhung chuan bucket 3/3 a khat. 3/3 chu bucket pumpui a khat vek tihna.
Alternatively,
Minute khata 1/3 an fill theih chuan minute thum chhung chuan bucket chu a khat nghal e (1/3 + 1/3 + 1/3 = 1)
December 8th, 2011 at 8:32 pm
Answer 2
Hei chuan summation of series (Arithmetic Progression) a hmang tlat.
Sigma X (summation) where limit tends to n = a + (a+1) + (a+2) + …. + an = 9808
= a1 + a2 + a3 + a3 …. + an
Summation of series chu kan hriat tawh angin,
Sn = n/2 (a1 + an) —-(1)
an = a1 + (n-1)d —-(2)
n hi page awm zat
a1 hi page hmasa ber
an hi page tawp ber
d hi difference between sequence a nia, mahse consectutive i tih avangin d equals 1, chuvangin telh a ngai in ka hrelova…
entirnan, phek 2 atanga phek 5 belh khawm chu 2 + 3 + 4 + 5 = 14
Hemi formula hmang chuan:
n = 4
a1 = 2
an = 5
therefore summation = (4/2) (2 + 5) = 14
Chutiang bawkin he problem ah unknown pathum a awm ta a…
n = phek engzah nge bo?
a1 = phek hmasa ber chu enge?
an = phek tawp ber chu enge?
n/2 (a1 + an) = 9808
n (a1 + an) = 19616
(1) leh (2) atangin kan hmuh theih chu
Sn = n/2 (2a1 + (n-1)d )
unknown pakhat chu kan peih bo ta a, chuan sawi tawh angin d=1 since they are consecutive term
Hence, Sn = n/2 (2a1 + (n-1) ) = 9808
n (2a1 + (n-1) ) = 19616 ————(#3)
He formula ah hian unknown pahnih chu a la awm cheu a, chuvangin excel spreadsheet ka hmang ta a
column ah phek awm zat ka drag thla a (1, 2, 3, … till 50)
Chuan row ah phek in tan na ka drag phei a (1, 2, 3, …. till 500)
Excel in hman thiam chuan vawihnih type a tawk mai a, a bak chu kha mi te sequence pahnih i select a i drag thlak emaw i drag phei chuan automatic in sequence a rawn siam mai a.
Chuan formula ah n (2a1 + (n-1) ) hi ka hmanga
Entirnan phek kua awm, phek in tanna chu page 2 a nih chuan = A14 * ((2*C5) + (A14-1)) ka tia, 108 a rawn chhuak mai a. (A dik tak chuan 54 a nia, mahse formula ah ka double vangin 108 a rawn chhuak ta a. excel sheet ah division formula ka hmang nasat duhloh vangin ka double mai a answer chu)
He formula hi, phek pumpui ah ka drag leh mai a, an value zawng zawng chu a rawn chhut chhuak nghal a.
Chumi zawh formula a answer 19616 (9808 double value) khi ka search keuh a, a hmu nghal a, chumi corresponding n value leh a1 value chu 32 leh 291 a lo nia.
Hence,
n = 32
a1 = 291
an = 322 (291 + 32 chu 323 a nia, mahse phek 291 atangin kan chhiar tan a)
Answer: Phek 291 na atanga phek 322 chu a kimlo.
December 8th, 2011 at 8:33 pm
Leh, Asteric, ka cheng 100 chu? Nuam eeeeeeeeeeee! 😀
Top up 100 man ka duh lo a nia, postpaid ka hmang. Cheng za chuan quarter khat a lei theih, a ti VaiVa an. 😀
December 8th, 2011 at 8:44 pm
Hetiang Formula ngai chi hi chu ka ngaihtuah buai peih vak lo.:-(
December 8th, 2011 at 8:46 pm
Pakhatna khi chu ka thiam e. Pakhatna chu Commerciai Mathematics ah kan zir thin a, Sandman chawh khi a dik thlap. Pahnihna erawh Arithmetic progression a ni thung a, ka chawk thiam lem lo :-O
December 8th, 2011 at 8:46 pm
awiha, ka tih chi anilo,beidawnthlak em mai
December 8th, 2011 at 8:49 pm
sandy chu a rilru a va chak e… (&) kei chu bucket size a sawi si lo va, ka chhut thiam lo ka lo ti a… 😉 :-$
December 8th, 2011 at 8:49 pm
^5, Commercial Mathematics tih zawk tur a ni e.
December 8th, 2011 at 8:50 pm
Eheu! Kei chu ka thluak chhaih ka phal tawh lo 😀 Thiamloh vang ni miahlo in…haha
Sandy thluak chu la active bawk maw 🙂
December 8th, 2011 at 8:51 pm
Pakhatna chhanna chu bucket a khat vek tawh a. Tihkhah a ngai leh tawh lo.
December 8th, 2011 at 8:55 pm
@sheldon, mihring thluak chu hman tam poh leh a chak tulh tulh e an ti. Kan thil hriat reng reng dot(.) ang in thluakah a inchhun kalh a, memory a expand zawk e an ti a lawm.
Pu C.Lalzarmawia khuavang tiat lawih a hriat tur :-O
December 8th, 2011 at 9:01 pm
Asteric, kei zawng ka nachhawka ei (doctor min chawh), Oxycodone ka kai tha chiai chuai lutuk a, nupui pawh chhaih peihlo chuan nidangah ka rawn chhaih sak mai ang che aw, i post hi. 😛 😉 hairehai
December 8th, 2011 at 9:08 pm
@lr, memory expend tul tawhlo, hriatsa pawh kan theihnghilh tawh ania 😀
December 8th, 2011 at 9:09 pm
Post publish anih hmain an lo attempt char2 bik a, ngihtuah ve hmain a chhanna a lo awm vek toh… :[ ka solve thei ang phei chu ka ti lawww.. 😀
tiang ram hnuk khoih lo lutuk ron post toh suh, @john_puia
December 8th, 2011 at 9:12 pm
#1,#2,#3
Sandman khian ka solve chhungin min chhan khal vek a lawm.Nula lam nise ka chhaih peih zawng tak a nia sin le 😀
December 8th, 2011 at 9:13 pm
@sheldon, Chinese putar pawh an tar tulh tulha, kungfu an thiam tulh tulh ni awm tak a ni.
Theihnghilh mai love a. 😀
December 8th, 2011 at 9:14 pm
No. 1 ka chawh ve dan:
A te berin a minute a duh zat =20min
A laihawl =12min
A lian ber = 5min
Chuvangin an vaia belhkhawma minute mamawh zat = 20-(12+5)
= 3mins
:-$
December 8th, 2011 at 9:20 pm
#17, a dik lo lutuk. Ngati nge 20-(12+5)=3 min, i tih ngawt? A vaia tangrualin a tih khi.
December 8th, 2011 at 9:21 pm
@14, i va ngam tan tan ve. Awm a awm ani lo maw? 😛
December 8th, 2011 at 9:25 pm
Har e..enge hlawh ka dawn ang? chulo chu ka chhut peih lo 😀 sweet 100 dah darh nuaih pawh engzat nge ka hre lo nia.. :-S
December 8th, 2011 at 9:26 pm
He post hi 8.30 ah publish ania, Sandy calculation sei zet 2 khi 8.32 ah kan hmu hman ve ve, a che rang lutuk, within 2 minutes ah a zo theilo…fair lo a awm chiang 😀 Asteric lawmman khi thluak hmangho zawng zawngin kan insem a ngai ang…haha 😛
December 8th, 2011 at 9:28 pm
#20, nula lenrei tum hi chu, an heti nuai tawh zel a, kan hrethiam che 😛
December 8th, 2011 at 9:28 pm
@sheldon…post chhuah rual chiah khan khi comment sei em em mai khi a rawn lut nghal. Software ala hmang zui 🙁 A last note(prize) khi ala EDIT zui bawk
A phakar lutuk tlat, a question awm zia khi schedule anih hma in mi rawn zawt chik lutuk. Admin ani sia lo hre ve nil nual rawh se tiin clue ka lo pe á¹euha…Ans nen a rawn publish nghal mawle 😮
December 8th, 2011 at 9:29 pm
a hnuaia mi khi ka lo hmu tel pek lo nih hi..khir top..ka hlawh lo mai ang
December 8th, 2011 at 9:32 pm
Answer:- 1. A chhanna chu 3 minutes a ni.
2. A chhanna chu page 291 atangin 322 telin a ni e.
December 8th, 2011 at 9:35 pm
Minute thum..35 – 2/11 = 3
Phek 291 to 322 chu a kimlo.
Sandman a solvena ka hmu lo reng reng ania aw 😛 😛
December 8th, 2011 at 9:37 pm
@Asteric, ‘sandy trick’ ka rawn expose man hi enge ka dawn ve dawn 😛
December 8th, 2011 at 9:37 pm
1 & 2 khi ring mai teh ang 🙂
December 8th, 2011 at 9:42 pm
Zawhna pakhatna khi Sandman chhanna khi ka ring a, zawhna pahnihna khi ka chawk ve mek.
December 8th, 2011 at 9:46 pm
Awlsam te in a lo tih theih reng alawm mawle.
December 8th, 2011 at 9:47 pm
#2na khi software hmang miah lovin chhang thei in awm em?
Sandman khian a formula hmana ‘a1’ leh ‘n’ value zawn nan microsoft Excel a hmanga, chuvangin a justify na khi ka pawm lo 😀 :thluak hlanga solve na ka hmu duh:
Exam mark pe tur ni ila ‘a1’ leh n lo chhuah dan k hre dawn si lova
@sheldon…lawman khi amah dil rawh, a siam a nih khi 😀
December 8th, 2011 at 9:50 pm
Mr Sandy hian a answer hi a pek hma in a google chiang mai! Eng site ah nge a luh chiah phei chu ka hre chuang law! Mahse,mi bright tak chu a ni ve hrim2. Sandman, ka fan(s) i ni
December 8th, 2011 at 9:59 pm
Naaaa a va fair love… minute hnih chhung leka rang tawka ka ngaihtuah leh type avangin ka lo thidang tawp vel a sin. Tunah ka rawn harh leh chiah…. excel hmanglo pawn a tih theih tho a lawm, mahse ka chhut vel peihlova…
December 8th, 2011 at 10:05 pm
Haha…sandy chuh, within 2 minutes a chhuthhuah atan chuan a sei lua. Ka lo expose che ania aw 😀
December 8th, 2011 at 10:06 pm
Kha khimi answer i hriat duh chuan:
Sheet tin in phek hnih a nei a, lehlam ve ve ah… chuan i veilamah even number (2, 4, 6 etc) a awm anga, i dinglamah (3, 5, 7, etc) a awm ang. Chuvangin odd number in a in tan ziah ang.
Page number kha hei hi lo ni ta se….
2n+1, whole number n thenkhat tan
2n+2, hei hi a lehlam phek number kha a ni
A sheet dawt leh chu
2n+3,
2n+4,
Chutiang chuan a kal zel ang. Phek i pawh thler chuan, hei hi i hmu ang
(2n+1) + (2n+2) + (2n+3) + (2n+4) + (2n+5) + (2n+6) + … + (2n+2x – 1) + (2n + 2x)
Hei hi an group tha leh la…
= (2n+1 + 2n+2x)*x
= (4n + 2x + 1) * x
9808 hi factor a ngai ta a, chuanin hei hi i hmu ang…
2*2*2*2*613
(4n+2x+1) hei hi odd number
(4n+2x+1) = 613
-> x = 16
(4n+32+1) = 613.
4n = 580
n = 145
->2n+1 = 291
2n+2x = 322
Chuvangin phek 291 atanga 322 chu a ni kimlo chu.
Thil pawimawh hriattur: Even number phek atangin tan pawh ni u la, hemi phek number tho hi i hmu chhuak ang.
Ti kha chuan, a fiah sawt em pu asteric? A fair thlap em pu asteric? A kim vek em pu asteric? Pawisa chu i rawn transfer tawh em pu asteric?
😀 nuam eeeeeeeeeeee! 😀
December 8th, 2011 at 10:06 pm
excel hmang miahlo in 291 atanga 322 inkar zawng hi calculator in ka belh a, a dik thlap. 😀
December 8th, 2011 at 10:11 pm
#17, an tangrual viau lawm ni.
A te berin minute 20 a duh a. Chuan a laihawl kan herh haw ve leh chuan minute 12 in hun a duh tlem anga, chumi awmzia chu minute 20 atang khan minute 12 kan paih anga(ie.20-12=8mins).
Chuan a lian ber kan herhhaw ve leh chuan minute 8 atang khian minute 5 kan paih ve leh anga (ie. 8-5= 3mins).
Chuan a chhuak chu minute 3 chiah a ni ta mai lawm ni.
20-12-5=3mins
or ’20-(12+5)= 3mins’ tih khi a tawi deuh mah mah i ti anih ka ring.
December 8th, 2011 at 10:11 pm
Shelly, minute 2 chhung leka ka type theih nachhan chu a rualin keyboard pahnih ka hmanga…
December 8th, 2011 at 10:14 pm
@sandman…hetah hian (4n + 2x + 1) odd ania x hi even a ni tih engtin nge i hriat 😀
(4n + 2x + 1) * x
(4n + 2x + 1) =613 khi engtia ti thei ngawt nge i nih 😀
December 8th, 2011 at 10:18 pm
@sandy, haha…kut 4 nen 😀 Calculation lamah chuan ka tluklo han han che, mahse typing speed hrim hrimah chuan ka cho che 🙂
December 8th, 2011 at 10:20 pm
i va han chik peih e awwwww…. hei, he link ah hian va en la, even a nih na chhan chu i hre mai ang. Hetiang zawhna ho te te chu ka chhang hmanlo, thil pawimawh tih tur ka nei 😀
http://bytes.com/topic/misc/answers/692417-pages-missing
December 8th, 2011 at 10:26 pm
Shelly, tunlai chuan thluak that ai mah in google thiam (eng keyword nge enter tur) tih hriat a pawimawh zawk 😀
December 8th, 2011 at 10:26 pm
#41 hahaha….nge i hriatthiam loh i lo paste a 😛
khi chhanna i lo paste khi a dik lo Ans chiah dik, x zawk pawh khian 613 tluk ve thei tho. kha lai line kha uncertainty nih kha 😀 bakah x khi enge ni tih sawi miah lo bawk pu sandy 😀
December 8th, 2011 at 10:29 pm
Kei chu ka google ve lo, manual in ka chhut 😀
@Asteric, Thluak chhaih hmasa a ka lawmman kha CASH in ka duh..haha 😛
December 8th, 2011 at 10:30 pm
😀
December 8th, 2011 at 10:30 pm
Ka account a rs 100 i ron deposit dan tur ringotah ka la buai.. 😀
December 8th, 2011 at 10:31 pm
ehiau, ReMpY leh Asteric te chuan joint bank account in lo hawng dun der tawh elauu?
December 8th, 2011 at 10:36 pm
gugul chak hlawm ve.
December 8th, 2011 at 10:38 pm
John.puia chu tihian kan chhang ve ang e (BaKcHeH in a ti! 😛 ) Herh hawn pathum I nei a, a kaw zau zawng a in an loh avangin a in haw tam hleih a. Chumi awmzia chu a kua a lo zau khan a pressure a tla hniam a, pressure a hniam chuan tui luan chak zawng (velocity) kha a lo sang ve thung ta a. Discharge a pe hnem tihna a lo ni ta a. Mahse, discharge pe hnem tur chuan pump emaw overhead tank emaw discharge head kha kan hriat a ngai phawt a.
A dawt lehah chuan, herhhawnna tin hawn lai khian tap dang khi khar a nih hmel bawk a. A mal mal a an thawhchhuah zat khi a chunga hriat ngai tih khian a huam bawk a. A zavai zawng zawng an lo tan rual takah chuan overhead tank ni ta se emaw syntax zem emaw ni ta se, a nemna tha (pressure) khi a tam sawt dawn a. (A mal mal bucket I dah khah chuan a bucket tawp ber rawh lai khian a dir teu teu tawh lo mai thei bawk). Tin, pump hman ni ta se, khawi atanga pump nge a nih a, a san zawng (disharge head) leh discharge capacity kha kan hriat leh hmasak phawt a ngai dawn a. Pump kha positive displacement pump nge a nih a dynamic pump tih pawh hriat tel theih se a tha ang.
Kan information neih ang zawng khi kan khawn khawm theih chuan ‘Rempuii hian nikhatah Mel 10 kal thei se, Asteric, Alejendro leh Sandman te hian tangrualin ni khatah Mel engzat nge an kal theih ang ? ” tih hi ka chhanna ni rawh se… 😛
Pahnihna chhanna chu… (ka battery a zo dawn.. nakinah ka rawn chhang leh ang) 😀
December 8th, 2011 at 10:39 pm
#47@sandman….ReMpy nen te chuan kan body awmna chiah nimai thuhmun lo 😉
December 8th, 2011 at 11:15 pm
Hetiang post hi Upsilon (epsilon pawh nilo) khan a rawn kui tiak a, kan uar thar ta hluai a ang. Thluak sen ngai a nih avangin a tha ka ti a, mahse, tam tan riau mai a. Kan ning ang tih ka hlau…
December 8th, 2011 at 11:19 pm
#51 lungngai suh, hei bak chu ka rawn ti tawh hrih lovang, phakar deuh an awm tlat
December 8th, 2011 at 11:23 pm
Asteric chu ka chhanna khi a dik leh dik loh sawi phawt la, pahnihna khi ka chhang ang
December 8th, 2011 at 11:34 pm
Thluak ava chhaih deuh ve hei chuan…:-D
December 8th, 2011 at 11:53 pm
Uhum… Tiang lampang bawk maw.
Company hovin engineers an recruit dawn hian hetiang aptitude test chu an uar khawp mai.
Lr-a khian ngaihtuah teh se. Hairehai.
1na khi chu a har lo a.
2na khian thluak chu a chhaih deuh dawn a nih khi. One Equation with 2unknown variables chawh a va ngaih hmel ve. Trial and error method lo chuan ka chawk thiam lo phawt.
December 9th, 2011 at 12:34 am
@Vaiva…pahnihna chu chhang leh phawt la a dik leh dik loh chu ka sawi ang
December 9th, 2011 at 1:55 am
2na khi ka try ve dawn:
AP formula hmangin equation siam ila
(n/2)(2a+n-1)=9808, n=no of pages, a=first page no
or, 2a+n-1=19616/n…….(1)
19616=2*2*2*2*2*613
n hi page kan tihthler zat a nih vangin even a ni ngei ngei tur a ni. chuan, n=even
eqn(1)-a LHS: 2a=even, n=even, 2a+n-1=odd.
Chuan, LHS=odd => RHS=odd
RHS=32*613/n odd integer ni tur chuan 19616, n-a kan sem chhuah chu 19616 factor zing a mi odd awm chhun 613 hi a nih ngei ngei a ngai a.
chuan RHS=613 means n=19616/613=32
chhuan eqn(1) hmangin a=291
last page=291+32-1=322 (AP last term)
1na khi chu awl em mai ti lo mai ang.
Khawi Rs 100.
December 9th, 2011 at 2:07 am
#35 -ah an lo chawk dik reng tawh a nih khi..
December 9th, 2011 at 3:18 am
mu ila..ka hlawk pui zawk ang a.
December 9th, 2011 at 3:31 am
|—HUIHAM—|