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UPSC Prelims

Mathematics

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Elementary Algebra / प्रारंभिक बीजगणित

Q16 2017, Elementary Algebra

There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?

भिन्त्र ऊँचाइयों के तीन खम्भे X, Y और Z हैं। तीन मकड़ियाँ A, B और C क्रमशः इन खम्भों पर एक ही समय पर चढ़ना शुरू करती हैं। एक प्रयास में A, X पर 6 cm चढ़ती है किन्तु 1 cm नीचे फिसल जाती है। B, Y पर 7 cm चढ़ती है किन्तु 3 cm नीचे फिसल जाती है। C, Z पर 6.5 cm चढ़ती है किन्तु 2 cm नीचे फिसल जाती है। यदि उनमें से प्रत्येक मकड़ी को खम्भे के शीर्ष तक पहुँचने के लिए 40 प्रयास करना पड़ता है, तो सबसे छोटे खम्भे की ऊँचाई क्या है?

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Pillar X: In one chance, A climbs on X by 6 cm but slips down 1 cm. Hence, in one chance A climbs 6 – 1 = 5 cm.

Height attained after 39 chances = 39 × 5 = 195 cm

Thereafter in the 40th and last chance it will climb 6 cm to reach the top. So, height of pillar X = 195 + 6 = 201 cm

Pillar Y: In one chance, B climbs on Y by 7 cm but slips down 3 cm. Hence, in one chance B climbs 7 – 3 = 4 cm.

Height attained after 39 chances = 39 × 4 = 156 cm

Thereafter in the 40th and last chance it will climb 7 cm to reach the top. So, height of pillar Y = 156 + 7 = 163 cm

Pillar Z: In one chance, C climbs on Z by 6.5 cm but slips down 2 cm. Hence, in one chance C climbs 6.5 – 2 = 4.5 cm.

Height attained after 39 chances = 39 × 4.5 = 175.5 cm

Thereafter in the 40th and last chance it will climb 6.5 cm to reach the top. So, height of pillar Z = 175.5 + 6.5 = 182 cm

So, height of the shortest pillar (i.e. pillar Y) = 163 cm

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