Exams

Let the two parallel sides of the trapezium be a cm and b cm. 

Then, a - b = 4 

And, 12×a+b×19=475=>a+b=50 

Solving (i) and (ii), we get: a = 27, b = 23. 

So, the two parallel sides are 27 cm and 23 cm.

Warm and hot are in the same meaning sense , so not so good is same as worse in meaning.

We know that the time difference between India and USA is 9 hrs 30 min.

India is 9:30 hrs ahead of USA.

Time in India = 4:15 + 9:30 = 13:45 PM.

Required Time after 18 hrs = 13:45 + 18 hrs = 7:45 AM.

Hence it is 7:45 AM on the next morning.

Man walked 6 km at 1.5 kmph, again he walked 8 km at speed of 2 kmph and 40 km at a speed of 8kmph
time taken indivisually:
=> 6/1.5 = 4 m
=> 8/2 = 4 m
=> 40/8 = 5 m

Average speed of man= total distance/ total time
=> 54/13 = 4213 kmph

5% is the rate of interest. 20% of the interest amount is paid as tax.

i.e  80% of the interest amount stays back.

 if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value.

The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest.

= 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32

The amount at the end of 3 years = 5000 + 624.32 = 5624.32

Let the number of apples in each tree of the 5 farmers be a, b, c, d,e respectively. Therefore total no of apples are 7a, 9b, 11c, 13d and 14e respectively.

Given,
7a+1 = 9b+3 = 11c-1 = 13d+3 = 14e-6 = x

9b+3 = 13d+3
===> 9b = 13d
so take b = 13 and d = 9

9b+3 = 9*13+3 = 120
ie, x=120

substituting
7a+1 = 120
7a = 119
a = 17

11c-1 = 120
11c = 121
c=11

14e-6 = 120
14e = 126
e = 9

Yields per tree in the orchards of d 3rd & 4th farmers= 11,9