Class 12th

Two runners ride from A to B a distance of 55 km, and the first arrives 30 minutes before the second. They then ride from B to A, the first giving the second a start of 4 km and yet arrive 6 minutes before him. Find the speed of A.

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Contributor-Level 10

Let the speed of A be x km/hr and speed of B be y km/hr, then:

$\frac{55}{x} = \frac{55}{y} - \frac{1}{2} . . . . . (1)$

Also, $\frac{55}{x} = \frac{51}{y} - \frac{1}{10} . . . . . (2)$

On solving both equation (1) & (2) we get x = 11 km/hr and y = 10 km/hr.

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New answer posted

7 months ago

There is a right circular cone of base radius 5 cm. This cone is cut into two portions by a plane parallel to its base such that the portion above the plane is a cone of base radius 3 cm and the portion below the plane has a height of 6 cm. Find the volume of the bottom solid.

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Contributor-Level 10

Volume of smaller cone

$= \frac{1}{3} π {(3)}^{2} * 9 = 27 π$

$= \frac{1}{3} π {(5)}^{2} * 15 = 125 π$

$\Rightarrow$ Volume of the solid = 125π – 27π = 98 π

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New answer posted

7 months ago

A Banana seller sells x dozen Bananas. If he had sold 100 dozen Bananas more at 20 paise a dozen less or if he had sold 120 dozen less at 30 paise a dozen more, he would have received the same amount for his Bananas. How many dozens does he sell?

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Contributor-Level 10

Px= (P-0.2) (x+100)= (P+0.3) (x-120)

Solving x=1000

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7 months ago

A shopkeeper buys 216 packets of biscuits at the rate of Rs. $\frac{x}{8}$ per pkt. He sells 8 dozen at the rate of Rs. 2.36 x per dozen and the rest at 16 $(\frac{x}{4} + 1)$ paise each. What is the value of profit?

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Contributor-Level 10

Total S.P. will be

$8 * [2.36 x] + \frac{16}{100} [\frac{x}{4} + 1] 120 = 18.88 x + 4.8 x + 19.2$

$= [\frac{x}{8}] 216 = 27 x$

Profit = 23.68x + 19.2 − 27x = 19.2 - 3.32x

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New answer posted

7 months ago

8 litres of wine are drawn from a cask and replaced by 8 litres of water. 8 litres of the mixture are next drawn and again replaced by 8 litres of water. If the ratio of wine to water in the cask is now 81 : 19, how much wine was in the cask at first? (There was no water in the cask at first.)

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Contributor-Level 10

Let there be x litres of wine in the beginning

${(\frac{x - 8}{x})}^{2} = \frac{81}{100}$

$\Rightarrow$ x = 80 litres

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7 months ago

S1, S2 and S3 are three contestants for a race of 2,000 metres. If S1 can give S2 a start of 100 metres and S3 a start of 138 metrse, then of how many metres would S2 give a start to S3 in a similar race?

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Contributor-Level 10

When S1 runs 1900 metres, S3 would run 1862 metres. Hence, the start given is 38/1900 * 2000 = 40 metres

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8 months ago

If the shortest distance between the straight lines 3(x – 1) = 6(y – 2) = 2(z – 1) and 4(x – 2) = 2(y - $λ)$ = (z – 3), $λ \in R$ is $\frac{1}{\sqrt[]{38}},$ then the integral value of is equal to:

(a) Let n denote the number of solutions of the equation z² + where z is a complex number. Then the value of $λ$ is equal to:

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alok kumar singh

Contributor-Level 10

$\frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 1}{3} . . . . . . . (i)$

$\frac{x - 2}{1} = \frac{y - λ}{2} = \frac{z - 3}{4} . . . . . . (i i)$

$\vec{O A} = (i + 2 j + k) \vec{O B} = (2 \hat{i} + λ \hat{j} + 3 \hat{k})$

$\vec{a} = 2 i + j + 3 k & \vec{b} = i + 2 j + 4 k$

$∴$ shortest distance = $| \frac{(\vec{O B} - \vec{O A}) . (\vec{a} * \vec{b})}{\vec{a} * \vec{b}} | = \frac{1}{\sqrt[]{38}}$

$\Rightarrow | 14 - 5 λ | = 1$

$\Rightarrow λ = 3 & \frac{13}{5}$

Integer value of $λ$ = 3

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New answer posted

8 months ago

If A : B = 5 : 6, B : C = 13 : 14, C : D = 9 : 4, find A : D.

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Raj Pandey

Contributor-Level 9

$(\frac{A}{B}) * (\frac{B}{C}) * (\frac{C}{D}) = \frac{A}{D}$

$\Rightarrow \frac{5}{6} * \frac{13}{14} * \frac{9}{4} = \frac{195}{112}$

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8 months ago

Rahul normally take 30 minutes to cover a particular distance. Having increased his speed by a% today, Rahul was able to cover the same distance in 10 minutes. What is the value of a?

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Raj Pandey

Contributor-Level 9

The new time is $\frac{1}{3}$ of the old time. If time becomes $\frac{1}{3}$ , then new speed should have been $\frac{3}{1}$ of the initial speed. Therefore

$\frac{3 S - S}{S} * 100 = 200 %$

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New question posted

8 months ago