Question:
A car driver increases the average speed of his car by 3 km/hr every hour. The total distance travelled in 7 hours if the distance covered in first hour was 30 km, is
A car driver increases the average speed of his car by 3 km/hr every hour. The total distance travelled in 7 hours if the distance covered in first hour was 30 km, is
Show Hint
When speed (or distance per hour) increases by a fixed amount each hour, use the sum of an AP: $S_n=\frac{n}{2}[2a+(n-1)d]$.
Updated On: Aug 13, 2025
- 266 km
- 273 km
- 280 km
- 287 km
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Distance covered each hour forms an arithmetic progression:
First hour $=30$ km; common difference $=3$ km.
Seven hourly distances: $30,33,36,39,42,45,48$.
Sum of AP: $S_n=\dfrac{n}{2}\,[2a+(n-1)d]$.
$S_7=\dfrac{7}{2}\,[2\cdot30+(7-1)\cdot3]=\dfrac{7}{2}\,(60+18)=\dfrac{7}{2}\times78=273$ km.
First hour $=30$ km; common difference $=3$ km.
Seven hourly distances: $30,33,36,39,42,45,48$.
Sum of AP: $S_n=\dfrac{n}{2}\,[2a+(n-1)d]$.
$S_7=\dfrac{7}{2}\,[2\cdot30+(7-1)\cdot3]=\dfrac{7}{2}\,(60+18)=\dfrac{7}{2}\times78=273$ km.
Was this answer helpful?
0
0
Top Questions on Arithmetic Progression
- If \( x_1, x_2, x_3, x_4 \) are in GP (Geometric Progression), then we subtract 2, 4, 7, and 8 from \( x_1, x_2, x_3, x_4 \) respectively, then the resultant numbers are in AP (Arithmetic Progression). Then the value of \( \frac{1}{24} (x_1 \cdot x_2 \cdot x_3 \cdot x_4) \) is:
- JEE Main - 2025
- Mathematics
- Arithmetic Progression
- If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to:
- JEE Main - 2025
- Mathematics
- Arithmetic Progression
- The 6th term of the AP \( \sqrt{27}, \sqrt{75}, \sqrt{147}, \ldots \) is:
- CBSE Compartment X - 2025
- Mathematics
- Arithmetic Progression
- The sum of the first 30 terms of an arithmetic progression is 930. If the first term is 2, what is the common difference of the progression?
- BITSAT - 2025
- Mathematics
- Arithmetic Progression
- The sum of the first 20 terms of an AP is 820. If the first term is 5, find the 20th term and the common difference.
- CBSE Compartment X - 2025
- Mathematics
- Arithmetic Progression
View More Questions
Questions Asked in CLAT exam
From a very early age, I knew that when I grew up, I should be a writer. I had the lonely child's habit of making up stories and holding conversations with imaginary persons, and I think from the very start my literary ambitions were mixed up with the feeling of being isolated and undervalued. I knew that I had a facility with words and a power of facing unpleasant facts, and I felt that this created a sort of private world in which I could get my own back for my failure in everyday life. I wanted to write enormous naturalistic novels with unhappy endings, full of detailed descriptions and arresting similes, and also full of purple passages in which words were used partly for the sake of their sound. I give all this background information because I do not think one can assess a writer's motives without knowing something of his early development.
His subject-matter will be determined by the age he lives in — at least this is true in tumultuous, revolutionary ages like our own — but before he ever begins to write he will have acquired an emotional attitude from which he will never completely escape. It is his job to discipline his temperament, but if he escapes from his early influences altogether, he will have killed his impulse to write. I think there are four great motives for writing, at any rate for writing prose. They are: (i) Sheer egoism: Desire to seem clever, to be talked about, to be remembered after death, to get your own back on grown-ups who snubbed you in childhood; (ii) Aesthetic enthusiasm: Desire to share an experience which one feels is valuable and ought not to be missed (iii) Historical impulse: Desire to see things as they are, to find out true facts and store them up for the use of posterity (iv) Political purpose: Desire to push the world in a certain direction, to alter other people's idea of the kind of society that they should strive after.
[Extracted with edits from George Orwell's "Why I Write"]- CLAT - 2025
- Reading Comprehension
- The right kind of education consists in understanding the child as he is without imposing upon him an ideal of what we think he should be. To enclose him in the framework of an ideal is to encourage him to conform, which breeds fear and produces in him a constant conflict between what he is and what he should be: and all inward conflicts have their outward manifestations in society. If the parent loves the child, he observes him, he studies his tendencies, his moods, and peculiarities. It is only when one feels no love for the child that one imposes upon him an ideal, for then one's ambitions are trying to fulfill themselves in him, wanting him to become this or that. If one loves, not the ideal but the child, then there is a possibility of helping him to understand himself as he is.
Ideals are a convenient escape, and the teacher who follows them is incapable of understanding his students and dealing with them intelligently; for him, the future ideal, the what should be, is far more important than the present child. The pursuit of an ideal excludes love, and without love no human problem can be solved. If the teacher is of the right kind, he will not depend on a method, but will study each individual pupil. In our relationship with children and young people, we are not dealing with mechanical devices that can be quickly repaired, but with living beings who are impressionable, volatile, sensitive, afraid, affectionate: and to deal with them, we have to have great understanding, the strength of patience and love. When we lack these, we look to quick and easy remedies and hope for marvellous and automatic results. If we are unaware, mechanical in our attitudes and actions, we fight shy of any demand upon us that is disturbing and that cannot be met by an automatic response, and this is one of our major difficulties in education.
(Extract with edits from "The right kind of Education" by J. Krishna Murti)- CLAT - 2025
- Reading Comprehension
- Education is not the amount of information that is put into your brain and runs riot there, undigested, all your life. We must have life-building, man-making, character-making assimilation of ideas.... If education were identical with information, the libraries are the sages in the world and encyclopaedias are the rishis. Getting by heart the thoughts of others in a foreign language and stuffing your brain with them and taking some University degree, you consider yourself educated. Is this education? What is the goal of your education? Open your eyes and see what a piteous cry for food is rising in the land of Bharata, proverbial for its food. Will your education fulfill this want?
We want that education by which character is formed, strength of mind is increased, the intellect is expanded and by which one can stand on one's own feet. What we need to study independent of foreign control, different branches of the knowledge that is our own, and with it the English language and Western science; we need technical education and all else that will develop industries so that men instead of seeking for service may earn enough to provide for themselves and save against a rainy day. The end of all education, all training, should be man-making. The end and aim of all training are to make the man grow. The training by which the current expression of will are brought under control and become fruitful, is called education. What our country now wants are muscles of iron and nerves of steel, gigantic wills, which nothing can resist, which can penetrate into the mysteries and secrets of the universe and will accomplish their purpose in any fashion, even if it meant going down to the bottom of the ocean, meeting death face to face.
There is only one method of attaining knowledge. It is by concentration. The very essence of education is concentration of mind. From the lowest to the highest man, all have to use the same method to attain knowledge. The chemist who works in the laboratory concentrates on elements to analyze them. Knowledge is acquired by concentration.
[Extracted with edits from "Education" by Swami Vivekananda]- CLAT - 2025
- Reading Comprehension
- Punctually at midday, he opened his bag and spread out his professional equipment, which consisted of a dozen cowrie shells, a square piece of cloth with obscure mystic charts on it, a notebook, and a bundle of palmyra writing. His forehead was dazzling with sacred ash and vermilion, and his eyes sparkled with a sharp, abnormal gleam which was really an outcome of a continual searching look for customers, but which his simple clients took to be a prophetic light and felt comforted. The power of his eyes was considerably enhanced by their position placed as they were between the painted forehead and the dark whiskers which streamed down his cheeks: even a half-wit's eyes would sparkle in such a setting. People were attracted to him as bees are attracted to cosmos or dahlia stalks, He sat under the boughs of a spreading tamarind tree which flanked a path running through the town hall park, It was a remarkable place in many ways: a surging crowd was always moving up and down this narrow road morning till night. A variety of trades and occupations was represented all along its way: medicine sellers, sellers of stolen hardware and junk, magicians, and, above all, an auctioneer of cheap cloth, who created enough din all day to attract the whole town. Next to him in vociferousness came a vendor of fried groundnut, who gave his ware a fancy name each day, calling it "Bombay Ice Cream" one day, and on the next "Delhi Almond," and on the third "Raja's Delicacy," and so on and so forth, and people flocked to him. A considerable portion of this crowd dallied before the astrologer too. The astrologer transacted his business by the light of a flare which crackled and smoked up above the groundnut heap nearby.
(Extracted with edits from "An Astrologer's Day" by R.K. Narayan)- CLAT - 2025
- Reading Comprehension
- The "Nari Shakti Vandan Adhiniyam", 2023 Act received near-unanimous support in both the Lok Sabha and the Rajya Sabha. The legislation mandates the reservation of one-third of all seats in the Lok Sabha, state legislative assemblies, and Delhi (as a union territory with an elected assembly) for women. This linking of the implementation of the Act to the implementing of two long-term exercises of census and delimitation, makes little sense to many, and sounds quite like empowerment delayed for now.
In a 2012 article 'Holding Up Half the Sky: Reservations for Women in India', Rudolf C Heredia breaks down the common misconceptions that cloud our understanding of women's political participation- "When women do attain a national leadership role it is often because they have inherited the mantle from their fathers ophusbands, rather than as persons in their own right and are then projected as matriarchs, part of the joint family, complementary to the patriarchy rather than a challenge to it."
In 'Equality versus Empowerment: Women in Indian Legislature', 2023, Soumya Bhowmick makes the case for going a step beyond quotas, and to turn our attention to the complexities that shape women's agency in the country. This, he argues, would require a bottoms-up approach, rather than merely handing out reservations in a top-down manner. "In a country like India with a considerably large heterogeneous population, the dissemination of legislative power would be insufficient to protect the interests of minority groups such as women, Scheduled Castes, and Scheduled Tribes." He concludes that "implementing the idea of reservation for women would bring about descriptive representation, but its transformation into substantive representation would depend on the change in the attitudes of the people."
While the reservation of one-third of seats for women belonging to the scheduled castes and tribes under the amendment to article 330a and 332 of the constitution is a welcome step, it remains to be seen whether it fully acknowledges the complex interplay of hierarchies, socio-political relationships which also affect the extent and nature of complications that surround effective realisation of women's politics for Indian politics to emerge as a truly emancipatory space.- CLAT - 2025
- National Affairs
View More Questions