Instructions

For the following questions answer them individually

Question 81

5 years ago the average age of a family which includes father, mother and a son was 35 years. 3 years ago the average age of father and mother was 46 years. What is the present age (in years) of the son?

Question 82

The cost price of 60 articles is same as the selling price of x articles. If there is a profit of 20%, then what is the value of x?

Question 83

A person scores 45% of the total marks in the exam and still fails by 40 marks. The passing percentage of the exam is 55%. What is the maximum marks of the exam?

Question 84

A man starts running from point P at 11:00 a.m. with a speed of 10 km/hr. He runs for 2 hours and then takes a 1 hour rest. He continues this process till he is caught by another man who starts at 2:00 p.m. from point P and runs non-stop at a speed of 15 km/hr towards the first man. At what time (in p.m.) will the first man be caught?

Question 85

The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23 : 7 respectively. What is rate of interest per annum (in %)?

Question 86

If $$\dfrac{x^{2}}{yz}+\dfrac{y^{2}}{zx}+\dfrac{z^{2}}{xy}=3$$, then what is the value of $$(x+y+z)^{3}$$ ?

Question 87

If $$\frac{x^\frac{1}{4}}{x^\frac{-1}{4}}=2$$, then what is the value of $$x^{81}+\frac{1}{x^{81}}$$ ?

Question 88

If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of $$(a^{2}+b^{2}+c^{2})$$ ?

Question 89

If $$x^{2}+\frac{1}{x^{2}}=1$$, then what is the value of $$x^{48}+x^{42}+x^{36}+x^{30}+x^{24}+x^{18}+x^{12}+x^{6}+1$$?

Question 90

In the given figure, PQRS is a trapezium in which PMIISN, NR = 9 cm, PS = 12 cm, QM= NR and NR = SN. What is the area $$(in cm^{2})$$ of trapezium?Â

CAT Averages, Ratios & Proportions

CAT Logarithms, Surds & Indices