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Quadratic Equations

Long Answer Type

201. A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by B to finish the work.

Suppose B alone takes x days to finish the work. Then, A alone can finish it in (x - 6) days.
Now, (A’s one day’s work) + (B’s one day’s work)
$equals 1 over straight x plus fraction numerator 1 over denominator straight x minus 6 end fraction$
and $space space space left parenthesis straight A plus straight B right parenthesis apostrophe straight s space one space day space work space equals space 1 fourth$
∴ $1 over straight x plus fraction numerator 1 over denominator straight x minus 6 end fraction equals 1 fourth$

$rightwards double arrow$ $fraction numerator straight x minus 6 plus straight x over denominator straight x left parenthesis straight x plus 6 right parenthesis end fraction equals 1 fourth$

$rightwards double arrow$ $fraction numerator 2 straight x minus 6 over denominator straight x squared minus 6 straight x end fraction equals 1 fourth$
$rightwards double arrow$ $8 straight x minus 24 space equals space straight x squared minus 6 straight x$
$rightwards double arrow space space space space space space space space space space space space space space space space space straight x squared minus 14 straight x plus 24 equals 0 rightwards double arrow space space space space space space space straight x squared minus 12 straight x minus 2 straight x plus 24 space equals space 0 rightwards double arrow space space space space space space space space space left parenthesis straight x minus 12 right parenthesis space left parenthesis straight x minus 2 right parenthesis space equals space 0 rightwards double arrow space space space space space space space space space space space space space space space space space space straight x space equals space 12 space space space or space space straight x space equals space 2$
But, x cannot be less than 6.
So, x = 12.
Hence, B alone can finish the work in 12 days.

195 Views

202. In a class, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects seperately.

93 Views

Short Answer Type

203. A trader bought a number of articles for Rs. 900. Five articles were found damaged. He sold each of the remaining articles at Rs. 2 more than what he paid for it. He got a profit of Rs. 80 on the whole transaction. Find the number of articles he bought.

420 Views

Long Answer Type

204. On a pillar 9 m high is perched a peacock. From a point 27 m away from the base of the pillar, a snake is coming to its hole at the bottom of the pillar. Seeing the snake, the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught?

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205. A two-digit number is such that the product of the digit is 14. When 45 is added to the number, the digits interchange their places. Find the number.

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Short Answer Type

206. A two digit number is seven times the sum of its digits and is also equal to 12 less than three times the product of its digits. Find the number.

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207. A two digit number is such that the product of its digits is 35. When 18 is added to the number, the digits interchange their places. Find the number.

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208. A two digit number is such that the product of its digit is greater then tens place digit by 8. If the number is more than the product of its digits by 10. Find the number.

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209. The number consists of two digits, unit place digit is greater than tens places digit by 8. If the number is more than the product of its digits by 10. Find the number.

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210. There are three consecutive positive integers such that, the sum of square of the first and the product of other two is 154. Find the integers.

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