MAT and IPM mega final test paper

Maths Aptitude Test ----- last 15 questions for std. VIII

IPM mega Finals practice Paper for Std. VIII

1.       If 4 kg of coffee is cost as much as 3 kg of tea, and 5 kg of tea cost as much as 10 kg of sugar. What is the price of each when 1 kg of coffee, 1 kg of tea and 1 kg of sugar together cost Rs 112.50?

2.       The price of cooking gas has increased by 20%. By what percent should the consumption come down so as not to increase his expenditure?

3.       A dishonest vendor professes to sell his goods at cost price but he uses a weight of 900 grams for a kg weight. Find his gain Percent?

4.       A reduction in 20% in the price of onions enables a purchaser to obtain 8 kgs more for Rs 80/-. What is the reduced price per Kg?

5.       1 kg of tea and 4 kg of sugar cost Rs 88.20, but if sugar prices rose by 50% and that of tea by 10% they would cost Rs 114.30. Find the price per kg of tea? Answer Rs 45

6.       A sells his goods 5% cheaper than B and 5% dearer than C. A man buys Rs 1000 worth of goods from A. Would it have been more or less profitable for him to have bought half thee goods from B and half from C?

7.       Find the simple interest on Rs 1000 from March 3^rd to July 27^th of the same year @ 5% per annum?

8.       An army consists of 12000 men and women. The average height of the men is 1.9 metres, that of the women is 1.8 metres and that of the army is 1.875 metres. Find the number of women in the army.

9.       If S = (1+ 3 + 5 + ........... 35) + (2 + 4 + 6..........+ 34), Then the Value of S is...........................

10.   Q as a percentage of P is equal to P as a percentage of (P + Q). Find Q as a percentage of P. (given square root of 5 = 2.236)

11.   Solve:       ^{(719×719+347×347−719×347)} / _{(719×719×719+347×347×347)} =.....................................

12.   Find the sum:  (1−¹/_n) + (1−²/_n) + (1−³/_n) +.................up to n terms=?

13.   What is the remainder when 17²⁰⁰ is divided by 18?  Answer 1

14.   If 7^{(x - y)} = 343 and 7^{(x + y)} = 16807, what is the value of x?

15.   What is the unit digit in (6324)¹⁷⁹⁷ × (615)³¹⁶ × (341)⁴⁷⁶?

Answer 4. 

 let x kgs be purchased for Rs 100.

So, now x kgs can be purchased for Rs 80.

So, for Rs 100, we can purchase (100/80)x kgs = 1.25x kgs

So, 25% more can be purchased for the same value.

but 25% is equivalent to 8 kgs

so, 100% is equivalent to (8/25) x 100 = 32 kgs

so, reduced price of onions = 80 / 32 = Rs 2.5 per kg

Answer 10.

given (q/p) x 100 = [p/(p + q)] x 100

or, q/p = p / (p + q)

now if q/p = y

we can re write the equation as y = 1/ ( 1+ y)

or y²  + y - 1 = 0

or, y = - 1/2 ±√5/2 

ignoring the negative value

y = 0.618 

so, (q/p) x 100 = 61.8%