In a restaurant response time taken for an order is directly proportional to square of number of all different letters of order placed by customer. Two friends Tom and Russell went to this restaurant. Tom ordered tea and pastry and Russell ordered coffee and cake. What is the ratio of response time for order of Tom to that of Russell?

Solution

Number of different letters in

Tom's order = 7 ⇒ (t, e, a, p, s, r, y)

Number of different letters in

Russell's order = 6 ⇒ (c, 0, f, e, a, k)

The ratio = (⁷⁄₅)² = $\frac{49}{36}$

How many liters of 3% hydrogen peroxide solution should be mixed with 6 liters of 30% hydrogen peroxide solution so as to get a 12% solution?

Solution

By rule of allegation
(Take diagonal subtraction)

A servant is paid a total of $100 and a turban for a full year service. If the servant works for only 9 months and received $65 and turban, what is the value of the turban?

Solution

You can make two equations

Subtracting 2 from 1.

∴ Salary for 12 months 35 × 4 = $140

∴ Cost of Turban is $40

0 is the center of the circle with AB as diameter. A circle with center C is drawn to touch semicircles on diameter AB. The radius of the circle with center C is

Solution

Let r be the radius of circle with centre C. Now OP = 6, CP = r ∴ OC = 6 - r

ΔOCD is a right angle triangle.

∴ By Pythagoras theorem, (CD)² = (OC)²+ (OD)²

∴ (r + 3)² = (6 - r)² + (3)²

r² + 6r + 9 = 36 + r² -12r + 9

18r = 36 ∴ r = 2cm.

There are 59 diagonals in a regular polygon of n sides. What is the value of n?

Solution

'n' is number of sides of a regular polygon ⇒ n is a natural number.

Num ber of diagonals in a regular polygon of n Sides = $\frac{n(n-3)}{2}$

$\frac{n(n-3)}{2}$ = 59 is not possible for a natural number n.

A student’s grade in a course is determined by 6 quizzes and 1 examination. If the examination counts thrice as much as each of the quizzes, what fraction of final grade is determined by the examination?

Solution

Let weightage for each quiz be z.

∴ Weightage for exam = 3x.

∴ Total weightage = 6x + 3x = 9x

Weightage of exam in final grade = $\frac{3x}{9x}$ = ¹⁄₃.

A, B, C are on a trip. A drives at 50 kmph for 1hr. B drives during next 2 hrs. at 48kmph. C drives for next 3 hrs at 52 kmph. They reach their destination after exactly 6 hrs. Their mean speed in kmph was?

Solution

$average\, speed=\frac{Total\, distance\, travelled}{Total\, time\, taken}$

$=\frac{50 + (2\times 48) + (3 \times 52)}{6}=\frac{302}{6}=50\frac{1}{3}km/hr.$

HCF and LCM of two numbers are 13 and 455 respectively. If one of the numbers lies between 75 and 125 then that number is?

Solution

Product of the numbers = HCF × LCM

HCF × LCM = 13 × 455 = 13 × 5 × 91 = 65 × 91

A two digit number is such that cube of its 24^th part is same as number obtained by interchanging digits of the number. What is the number?

Solution

By Hit and Trial.

72 x $\frac{1}{24}$ = 3 → (3)³ = 27, 72 interchanged i.e. 27

2! + 4! + 6! + 8! + 10!…………+ 100! when divided by 3 would leave a remainder?

Solution

Note that each of the terms except 2! is divisible by 3. Therefore remainder is 2.

Attempted

0

Correct

0

Wrong

0

Complete

Attempted

Wrong

Correct