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CBSE Class 10 Mathematics Solved Question Paper 2018

Long Answer Type

31.

The following distribution gives the daily income of 50 workers of a factory:

Daily Income (In) 100-120 120-140 140-160 160-180 180-200

Number of workers 12 14 8 6 10

Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.

32.
A motor boat whose speed is 18 km/hr in still water 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Let the speed of stream be x km/hr

Now, for upstream,speed = (18-x) km/hr

$∴ time taken = (\frac{24}{18 - x}) hr$

Now, for downstream;speed = (18 +x) km/hr

$∴ time taken = (\frac{24}{18 + x}) hr$

Given that,

$\frac{24}{18 - x} = \frac{24}{18 + x} + 1 - 1 = \frac{24}{18 + x} - \frac{24}{18 - x} - 1 = \frac{24 [(18 - x) - (18 + x)}{(18)^{2} - x^{2}} - 1 = \frac{24 [- 2 x]}{324 - x^{2}} - 324 + x^{2} = - 48 x x^{2} + 48 x - 324 = 0 x^{2} + 54 x - 6 x - 324 = 0 (x + 54) (x - 6) = 0 x = - 54 o r x = 6 x = - 54 k m / h r x = 6$

Speed can never be negative, -54 km/hr

hence speed of the stream 6 km/hr

33.

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. It takes 3 hours to complete the total journey, what is the original average speed ?

34.

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.