Question

Solve the following:-
1. A group of people were asked to choose their favourite fruit . One
fourth chose apple , one third chose banana and two fifth chose
orange and three people chose litchi. How many people were there in
the group ?
2. Shika and Neetu are friends . They both are very health conscious . They jog daily in the morning around a rectangular park of area is x2 + 6x + 8 a) Factorise the area of the park and find its dimensions b) Do you think jogging is a good habit or it is just a wastage of time and energy. 3. Seema borrowed Rs12000 from Jamshed at 6% per annum simple
interest for 2 years . Had she borrowed this sum of 6% per annum
compound interest , what extra amount would she has to pay?
4. A shirt was sold for Rs 884 after allowing a discount of 15% on the marked price . Find the marked price of the shirt. 5. A water tank casts a shadow 21 m long. A tree of height 9.5 m casts a shadow 8 m long at the same time. The lengths of the shadows are directly proprotional to their heights. Find the height of the tank.

Answer 1

1) let's say there are x people in total:
x/4 chose apple
x/3 chose banana
2x/5 chose orange
3 chose litchi
we can now see that the sum of these 4 terms will give us x,
x/4 + x/3 + 2x/5 + 3 = x
hence , solve this equation (it's easy)
solution: x/4+ x/3 = 7x/12
7x/12 + 2x/5 = 59x/60
so we have:
59x/60 + 3 = x
3 = x - 59X/60
3 = (60x-59x)/60
3*60 = x = 180


2) x²+ 6x +8
x² + 2x + 4x + 8
x(x+2)+4(x+2)
(x+2)(x+4)

3) simple interest per year is 12000 x 6/100
which is 720 rupees
hence after two years the amount will be 12000 + 2(720)
which is 13440.
now for the compound interest case , for first year the interest will be 720,
now the amount after the end of 1 year will be 12720, now 6% of that is , 763.2.
add that to the amount to get 13483.2.
now see the difference between the simple interest sum and this one,
it is clearly 13483.2-13440 = 43.2₹

4) let marked price be x,
after a 15% discount, the price would become 85x/100.
now this is equal to 884
85x/100 = 884
x = 884*100/85
x = 1040₹
therefore market price is 1040₹

5) if A is directly proportional to B we know that A = kB where k is some constant.
let the real height be X and shadow length be Y.
for the tank : X1 = kY1
Y1 is 21 m
hence X1 =21Y1
for the tree:
X2=9.5
Y2=8
therefore 9.5 = k * 8
find k , k = 9.5/8 = 1.1875
put the value of k in the first equation.
X1 = 1.1875*21 = 24.9375