P and Q are two fixed points 10 cm apart, and R is a point on PQ such that PR = 6 cm. By what percentage is the length of QR decreased when the length of PR is increased by 5%?

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Accepted Answer

Step 1: Given PQ = 10 cm, PR = 6 cm, so QR = PQ - PR = 10 - 6 = 4 cm.

Step 2: PR is increased by 5%, so new PR = 6 + 5% of 6 = 6 + 0.3 = 6.3 cm.

Step 3: New QR = PQ - new PR = 10 - 6.3 = 3.7 cm.

Step 4: Decrease in QR = original QR - new QR = 4 - 3.7 = 0.3 cm.

Step 5: Percentage decrease in QR = (decrease/original QR) × 100 = (0.3/4) × 100 = 7.5%.

Therefore, the length of QR is decreased by 7.5%.

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