Question
Mohit starts from point Y and drives 6 km towards south.
He then takes a left turn, drives 23 km, turns right and drives 27 km. He then takes a right turn and drives 11 km. He takes a right turn, drives 13 km. He then turns right, drives 19 km, turns left and drives 20 km to stop at point Z. How far (shortest distance) and towards which direction should he drive in order to reach point Y again? (All turns are 90 degrees turns only unless specified.)Solution
Place Y at the origin (0,0)(0,0) ( 0 , 0 ) . Take north as +y+y + y , east as +x+x + x .
Follow Mohit’s moves step by step:
-
6 km south → (0,−6)(0,-6) ( 0 , − 6 )
-
Left (facing south → left = east) 23 km → (23,−6)(23,-6) ( 23 , − 6 )
-
Right (facing east → right = south) 27 km → (23,−33)(23,-33) ( 23 , − 33 )
-
Right (facing south → right = west) 11 km → (12,−33)(12,-33) ( 12 , − 33 )
-
Right (facing west → right = north) 13 km → (12,−20)(12,-20) ( 12 , − 20 )
-
Right (facing north → right = east) 19 km → (31,−20)(31,-20) ( 31 , − 20 )
-
Left (facing east → left = north) 20 km → (31,0)(31,0) ( 31 , 0 ) = point Z
So Z is at (31,0)(31,0) ( 31 , 0 ) and Y is at (0,0)(0,0) ( 0 , 0 ) . The displacement from Z to Y is (−31,0)(-31,0) ( − 31 , 0 ) , i.e. 31 km due west.
Answer: He must drive 31 km towards the west to return to point Y.
In a mixture of milk & water, 70 litres water is mixed due to which ratio changes from 3 : 4 to 1 : 3. Find initial quantity of mixture. (in litres)
A 1000 ml mixture contains milk and water in the ratio of 7:3. 10% of the mixture is removed and some water is added so that the new ratio of milk to wa...
40 litres of a solution contains 20% milk. After adding 'd' litres of pure milk, the quantity of milk becomes 150% more than the quantity of water. If m...
A solution contains acid and water in the ratio of 3:11. If 10 litres of acid is added to the solution, the ratio of acid to water becomes 1:2. What was...
There is 275 litres of mixture of milk and water in a jar. The ratio of quantity of milk to water in the jar is 8:3, respectively. If ‘x’ litres of ...
- Quantity of honey is 55% more than that of water in 204 litres mixture (honey + water). If 24 litres honey is added, then find the quantity of honey in the...
A mixture of Silver and Nickel contains 25% Silver. If 10 kg of Silver is added, then Silver becomes 50% of the Nickel. Find the initial quantity of Sil...
Vessels A and B contain mixture of milk and water in the ratios 3:7 and 5:3 respectively. In what ratio should quantities of mixtures be taken from A an...
A mixture contains milk and water in the ratio of 7:12. When 12 litres of milk and 6 litres of water are added to the mixture, the new ratio of milk to ...
- Mixtures A and B have milk and water in ratio 3:5 and 2:3 respectively. 40 ml from A and 45 ml from B are mixed. Find the percentage of water in the final ...
Relevant for Exams:
