Question 1.
If some distance is traveled at a speed of ‘x’ km/h and the same distance is traveled at a speed of ‘y’ km/h. Then, the average speed during the whole journey:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdQQLE7hZnnwu-OzJYVb1I3MhpNVIyUxHoTpWrxf11BLfaeHsKbEM1jWDYen5lLVGKltKHv2tOhNvAjUZVyQ3QERBrZcUrlQ4JYJGlpMxqimADZdCizLeNjgu9ZtxO1DDmTJwJhHJSCxA/s200/1.png)
Example: If the distance between Goa to Delhi is 750 km. A person goes at a speed of 60 km/h and returns at a speed of 40 km/h. Find the average speed.
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirDL5Gj0LFyZCS9PuXkiNRu0yhBWKi59vAnpWJ9fXWAfyUQeYn00dBbL6qJiB32Zh9AIMufCSVI2LGNlk4UesM4lMXPCYJviiZ1ebfnQ5MCqvLuah3ooTW_Ba6q34hU25b_q5VNcjJwFM/s320/2.png)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdQQLE7hZnnwu-OzJYVb1I3MhpNVIyUxHoTpWrxf11BLfaeHsKbEM1jWDYen5lLVGKltKHv2tOhNvAjUZVyQ3QERBrZcUrlQ4JYJGlpMxqimADZdCizLeNjgu9ZtxO1DDmTJwJhHJSCxA/s200/1.png)
Example: If the distance between Goa to Delhi is 750 km. A person goes at a speed of 60 km/h and returns at a speed of 40 km/h. Find the average speed.
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirDL5Gj0LFyZCS9PuXkiNRu0yhBWKi59vAnpWJ9fXWAfyUQeYn00dBbL6qJiB32Zh9AIMufCSVI2LGNlk4UesM4lMXPCYJviiZ1ebfnQ5MCqvLuah3ooTW_Ba6q34hU25b_q5VNcjJwFM/s320/2.png)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif)
Question 2.
If the distance is different than average speed is:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicXjXE3oC55aAKBGxKsuk9x1M3mN82iDak_x4H5Kl04aIqkIYSJtAyJvuymWI3_pQO2AUO5K8gnYZXZFmbM0b29t_GDQFoRq2JrXhKUeAF_92gOSa-MyodiydkV8Sp4intk9T1M65kEXU/s320/3.png)
Example: If the speed of the bus is 30 km/h for the 90 km and 35 km/h for the distance of 70 km. Find the average distance.
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicXjXE3oC55aAKBGxKsuk9x1M3mN82iDak_x4H5Kl04aIqkIYSJtAyJvuymWI3_pQO2AUO5K8gnYZXZFmbM0b29t_GDQFoRq2JrXhKUeAF_92gOSa-MyodiydkV8Sp4intk9T1M65kEXU/s320/3.png)
Example: If the speed of the bus is 30 km/h for the 90 km and 35 km/h for the distance of 70 km. Find the average distance.
Solution:
If the speed ratio between P and Q is a:b, so to cover the same distance the ratio between times taken by them will be
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3ZBxJsyjgTH_Kb_FrOUz0H61psq3eawaNwj4bm0v9J4Fy_JXyagXCLNhX3I-sOXABXeev9UIBrMP4BfNsPOfPZ7XOdnk2h1EYXanugVGaj103my_hPj7a6gjkYnkYW-7uEzs8Zg_7BYk/s1600/5.png)
Example: The ratio between the speed of two cars is 6:8. If the second car covers a certain distance in 9 hours, then find the time taken by the first car to cover the same distance.
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcNLTLlwyUvZ7doas-zKsYTHYv9SBuboUHr6YO5mzYEbF79ezaP8FP3joniVxakWGqsxDvSWoi_qBMxdp_8_e9oQ3tSoIbwjJJDIN4IZfgnfmNibCYyedxWH94N5cvdYZw34nMLSUpwx4/s320/6.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3ZBxJsyjgTH_Kb_FrOUz0H61psq3eawaNwj4bm0v9J4Fy_JXyagXCLNhX3I-sOXABXeev9UIBrMP4BfNsPOfPZ7XOdnk2h1EYXanugVGaj103my_hPj7a6gjkYnkYW-7uEzs8Zg_7BYk/s1600/5.png)
Example: The ratio between the speed of two cars is 6:8. If the second car covers a certain distance in 9 hours, then find the time taken by the first car to cover the same distance.
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcNLTLlwyUvZ7doas-zKsYTHYv9SBuboUHr6YO5mzYEbF79ezaP8FP3joniVxakWGqsxDvSWoi_qBMxdp_8_e9oQ3tSoIbwjJJDIN4IZfgnfmNibCYyedxWH94N5cvdYZw34nMLSUpwx4/s320/6.png)
Question 4.
To find the time of halts when the speed with stoppages is
a km/h and speed without stoppages b km/h:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRH6Dn78RlJMg2AsTRsnNeAgnwj5t9Vnl9aFPvLulKw9aQ46zDRUhvGZo2fBvnC9J-yHAWHm7upIreHnYgbMmjPo5OngecE5c161qllBwu0OTkO5VAdkgfpFbvIKEzRWAhIr9uA_N9J1c/s320/7.png)
Example:A man running on a road without any stoppage at an average speed of 100 km /hr, and he covers the same distance with stoppage at an average speed of 80 km/hr. How many minutes per hour does boy stop?
Solution:
a km/h and speed without stoppages b km/h:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRH6Dn78RlJMg2AsTRsnNeAgnwj5t9Vnl9aFPvLulKw9aQ46zDRUhvGZo2fBvnC9J-yHAWHm7upIreHnYgbMmjPo5OngecE5c161qllBwu0OTkO5VAdkgfpFbvIKEzRWAhIr9uA_N9J1c/s320/7.png)
Example:A man running on a road without any stoppage at an average speed of 100 km /hr, and he covers the same distance with stoppage at an average speed of 80 km/hr. How many minutes per hour does boy stop?
Solution:
Question 5.
A man walks at x/y speed of his actual speed reaches his destination z mint later. To cover this distance actual time is:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLU0zgKnDpzMALm_xN0MKo2PsXEhyphenhyphenvIZWnoO8qPFdYct5BhBD6crDq9ZPTOqh8MphYHh9jAzJFqZyXuUFwzzPwai6eCWN2wvi2udjfCziSquR5lrRFXyK8N3fMeJz2L4lOdZKXJUWJI1U/s200/9.png)
Example: Walking at 3/4th of usual speed, A person is late by 10 minutes. Find the usual time.
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFBn5QlssV__Hmr7VQMwuElUREZoJHcy37v2tUDJ51DlwA1vf5GobaHc5ICTM43qrlyzNBFuYHEydMwqgMbhZ-FHBfa6UhWkI6WQrzUZOkpTqRFDm9qXUS1g3gf0QkK-vHW1Agvxywf3k/s320/10.png)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image028.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLU0zgKnDpzMALm_xN0MKo2PsXEhyphenhyphenvIZWnoO8qPFdYct5BhBD6crDq9ZPTOqh8MphYHh9jAzJFqZyXuUFwzzPwai6eCWN2wvi2udjfCziSquR5lrRFXyK8N3fMeJz2L4lOdZKXJUWJI1U/s200/9.png)
Example: Walking at 3/4th of usual speed, A person is late by 10 minutes. Find the usual time.
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFBn5QlssV__Hmr7VQMwuElUREZoJHcy37v2tUDJ51DlwA1vf5GobaHc5ICTM43qrlyzNBFuYHEydMwqgMbhZ-FHBfa6UhWkI6WQrzUZOkpTqRFDm9qXUS1g3gf0QkK-vHW1Agvxywf3k/s320/10.png)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image028.gif)
Question 6.
A man walks at x/y speed of his actual speed reaches his destination z mint early. To cover this distance actual time is:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtJPYW2sQp20gjjiahV1Fwc7R6rSrdNmP7ZGZDTCCgVHwezfHYkH7YfTf68VQj8BnZ93pgNw18nq7bsZrYX4m9R8Kz9bax1VJIF-Plu7q9Dclvh-5-rytwMYE7bv2CMUHnV5evHaMkG64/s200/11.png)
Example: Walking at 6/5th of usual speed, A person reached early by 5 minutes. Find the usual time.
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHP3ARYKVFwewPU-boA0vJJ0nLHirOtMY1kr-xUwtP2ZMQp1dxCRdNXO2F2M76UeFHvR6M2mViPGgSvxB3LK2moazpbNSWKATcZ9igATFkaz5vjgWQ7_RRLSfIJxJn1DdulDMRDkhzRsY/s320/12.png)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image036.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtJPYW2sQp20gjjiahV1Fwc7R6rSrdNmP7ZGZDTCCgVHwezfHYkH7YfTf68VQj8BnZ93pgNw18nq7bsZrYX4m9R8Kz9bax1VJIF-Plu7q9Dclvh-5-rytwMYE7bv2CMUHnV5evHaMkG64/s200/11.png)
Example: Walking at 6/5th of usual speed, A person reached early by 5 minutes. Find the usual time.
Solution:
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image036.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHP3ARYKVFwewPU-boA0vJJ0nLHirOtMY1kr-xUwtP2ZMQp1dxCRdNXO2F2M76UeFHvR6M2mViPGgSvxB3LK2moazpbNSWKATcZ9igATFkaz5vjgWQ7_RRLSfIJxJn1DdulDMRDkhzRsY/s320/12.png)
Question 7.
A & B start moving towards each other at same time. After meeting each other, they reach their destinations after ‘a’ and ‘b’ hrs respectively.
A’s Speed: B’s Speed = √b: √a
Example: Two trains, one from Delhi to Pune and the other from Pune to Delhi, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. What will be the ratio of their speeds?
Solution:
A:B = √b : √a
A:B = √9 : √4
A:B = 3:2
A’s Speed: B’s Speed = √b: √a
Example: Two trains, one from Delhi to Pune and the other from Pune to Delhi, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. What will be the ratio of their speeds?
Solution:
A:B = √b : √a
A:B = √9 : √4
A:B = 3:2
Question 8.
A man/train leaves from A at x1 AM and reaches Q at x2 AM. Another man/train leaves from Q at y1 AM and reaches P at y2 PM. They will meet:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi90UQb74Zfnln-_HF2b7u_5tuLBkX3ZPXq13zX6Ah8-K06Yf38wfdDo7WEmdd9VCqxsFPcE9V2395dIR2rBm2urovwJQPG-sbZzwIutUUe7P81nIXH60HERfA41rd30SMzSzGNhMrEoTQ/s320/13.png)
Example: A train leaves from Bombay at 6:30 AM and reaches Jaipur at 10:30 AM. Another train leaves from Jaipur at 9 AM and reaches Delhi at 12:30 PM. When they will meet?
Solution:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi90UQb74Zfnln-_HF2b7u_5tuLBkX3ZPXq13zX6Ah8-K06Yf38wfdDo7WEmdd9VCqxsFPcE9V2395dIR2rBm2urovwJQPG-sbZzwIutUUe7P81nIXH60HERfA41rd30SMzSzGNhMrEoTQ/s320/13.png)
Example: A train leaves from Bombay at 6:30 AM and reaches Jaipur at 10:30 AM. Another train leaves from Jaipur at 9 AM and reaches Delhi at 12:30 PM. When they will meet?
Solution:
If the distance between A to B is D km. Two persons P and Q travel from points A to B, with the speed of 'a' and 'b' respectively and Q reaches B first, returns immediately and meets P at X, then
Distance traveled by P (from points A to X) =![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image052.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk2EG5BbseAU9FDDMLVwVtL7kbGAoKhFghUpJiSoCczMQdur9CZvcAyE7lg0KVG8LeRn-Y-2hy80uzr31I7GWOtCPBb960AnJu3d9rMUH43JQ-LrTASzdMdh4v31DYHLg8kcb8BHJWAb8/s1600/Capture.PNG)
Example: Suhail and Meetu travel from point A to B, a distance of 48 km, at 7 km/ h and 9 km/ h, respectively. Meetu reaches B first and returns immediately and meets Suhail at R. Find the distance from points A to R.
Solution:
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image054.gif)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image056.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmPkDhvmV6nq94EFYj_lEkY2WcQnZcMFADHiE4G1CVyUUTgIuCmO-rCj5HeqzgJ-tnoFN5zzCmOgSntu5YJDuecTYFIePn34yXPr0IQRg21yH6CZ1K9nHosYGRJIONkxIEfsx2wCvmJps/s400/15.png)
Distance traveled by P (from points A to X) =
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image052.gif)
Example: Suhail and Meetu travel from point A to B, a distance of 48 km, at 7 km/ h and 9 km/ h, respectively. Meetu reaches B first and returns immediately and meets Suhail at R. Find the distance from points A to R.
Solution:
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image054.gif)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image056.gif)
![](file:///C:/Users/MYPC~1/AppData/Local/Temp/msohtmlclip1/01/clip_image058.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmPkDhvmV6nq94EFYj_lEkY2WcQnZcMFADHiE4G1CVyUUTgIuCmO-rCj5HeqzgJ-tnoFN5zzCmOgSntu5YJDuecTYFIePn34yXPr0IQRg21yH6CZ1K9nHosYGRJIONkxIEfsx2wCvmJps/s400/15.png)
Question 10.
Relative Speed:
(i). If two objects are moving in the same direction with the speeds of a km/h and b km/h then their relative speed is |a‐b|.
(ii). If two objects are moving in opposite direction with the speeds of a km/h and b km/h then their relative speed is (a+b).
Example: 2 men A and B started from a place P walking at 4 km/h and 3 km/h respectively. How many km will they be a part at the end of 1 hour?
(i) If they walk in the same direction.
(ii) If they walk in opposite direction.
Solution:
(i): Relative speed = Ia-bI
= I 4-5 I
= 1 km/h
(i). If two objects are moving in the same direction with the speeds of a km/h and b km/h then their relative speed is |a‐b|.
(ii). If two objects are moving in opposite direction with the speeds of a km/h and b km/h then their relative speed is (a+b).
Example: 2 men A and B started from a place P walking at 4 km/h and 3 km/h respectively. How many km will they be a part at the end of 1 hour?
(i) If they walk in the same direction.
(ii) If they walk in opposite direction.
Solution:
(i): Relative speed = Ia-bI
= I 4-5 I
= 1 km/h
(ii): Relative speed = a+b
= 4+5
= 9 km/h
= 4+5
= 9 km/h
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