QUESTION

CSAT

Medium

Maths

Prelims 2017

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?

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Explanation

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 = $39 \times 5 = 195$ cm. Thereafter in the 40th and last chance it will climb 6cm to reach the top. So, height of pillar X = $195 + 6 = 201$ cm.

Pillar Y: In one chance, B climbs on Y by 7cm but slips down 3cm. Hence, in one chance B climbs $7 - 3 = 4$ cm. Height attained after 39 chances = $39 \times 4 = 156$ 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 = $39 \times 4.5 = 175.5$ 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.