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A square park \(P Q R S\) of side \(90 \mathrm{~m}\) is so located that its diagonal \(P R\) is from north to south and the corner \(Q\) is to the west of \(S\). Radha and Mohan start walking along…

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A square park PQRSP Q R S of side 90 m90 \mathrm{~m} is so located that its diagonal PRP R is from north to south and the corner QQ is to the west of SS. Radha and Mohan start walking along the sides from QQ and RR respectively in clockwise and anti-clockwise directions with speeds of 8 km/hr8 \mathrm{~km} / \mathrm{hr} and 10 km/hr10 \mathrm{~km} / \mathrm{hr}. Where will they cross each other the second time ?
  1. On PSPS at a distance of 30 m30 \mathrm{~m} from PP
  2. On QRQ R at a distance of 10 m10 \mathrm{~m} from QQ
  3. On PSPS at a distance of 30 m30 \mathrm{~m} from S\mathrm{S}
  4. On QRQR at a distance of 10 m10 \mathrm{~m} from R\mathrm{R}

Answer and explanation

Correct answer: D - On \(QR\) at a distance of \(10 \mathrm{~m}\) from \(\mathrm{R}\)
With P north, R south, Q west and S east, the clockwise order is P-S-R-Q. Radha (8 km/h) goes Q->P->S... and Mohan (10 km/h) goes R->S->P..., so they start 270 m apart along their paths. First meeting: Radha covers 270 x 8/18 = 120 m (30 m past P on PS). Second meeting: a further 360 x 8/18 = 160 m, 280 m in all from Q (Q-P 90, P-S 90, S-R 90, then 10 m along RQ). That is on QR, 10 m from R.

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