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The ratio between the present ages of P and Q is 5 : 7 respectively. If the difference between Q's present age and P's age afler 6 years is 2, what is the total of P's and Q's present ages?
Let the present ages of P and Q be 5x years and 7x years respectively.Then7x(5x+6)=22x=8x=4.Required sum= 5x+7x=12x=12×4=48 years.
The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side is
Ratio of sides = 13 : 14 : 15
Perimeter of triangle = 168 cm
Let the sides are 13x, 14x, and 15x
∴ 13x + 14x + 15x = 168
⇒ 42x = 168
⇒ x = 4
∴ sides are 13 x 4 = 52 cm
14 x 4 = 56 cm
15 x 4 = 60 cm
s = sum of sides/2 = 168/2 = 84
∴ Area of the triangle
Let BL be altitude on the largest side AC of A ABC
Area of Δ ABC = 1344 cm^{2}
⇒ 1/2 x base x altitude = 1344 cm^{2}
⇒ 1/2 x AC x BL = 1344 cm^{2}
⇒ 30 BL = 1344
⇒ BL = 1344/30 = 44.8 cm
A sum borrowed under Compound Interest doubles itself in 10 yrs. When will it become fourfold of itself at the same rate of interest?
2 → 10 years
4(=2^{2}) → 10 x 2 i.e. 20 years
If α and β are the roots of the quadratic equation x^{2} − 2 x + 3 − 0, then α^{3}β + αβ^{3}
α + β = 2 ; α β = 3
α^{2} + β^{2} = (α + β)^{2} − 2 α β = 4 − 6 = − 2
An angle is divided into the two parts α and β such that tan α = 1/2 and tan β = 2. The measure of the angle is
A body of mass 2 kg is at rest. The force required to produce a velocity of 2 ms^{1} in 4 seconds is
v = u + at; u = 0 (inital velocity)
2 = 0 + a.4
a = 1/2 m ∕ s^{2}
F = m . a = 2 x 1/2 = 1 N .
ABC is a triangle in which BC is produced to D. In case ∠A:∠B:∠C::3:2:1 and AC⊥CE, the measure of ∠ECD is
2 Pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is
Work done by the waste pipe in 1 minute = 1/15  ( 1/20 + 1/24 )
= ( 1/15  11/120 )
=  1/40
[ve sign means emptying]
∴ Volume of 1/40 part = 3 gallons
Volume of whole = (3 x 40) gallons = 120 gallons
The smallest integer, which when substracted from both the terms of 6:7 gives a ratio less than 16:21, is
If x be the required integer, then,
6  x/7  x < 16 21
or, 126  21x < 112  16x
or, 5x > 14
or, x > 14/5 = 2.8
The smallest possible integer x = 3
Income of a company doubles after every one year. If the initial income was Rs. 4 lakhs, what would be the income after 5 years?
Income after 1 year = Rs.(4 x 2^{1}) lakhs
Income after 2 years = Rs.(4 x 2 x 2)lakhs = Rs.(4 x 2^{2})lakhs
∴ Income after 5 years = Rs.(4 x 2^{5})lakhs
= Rs.128 lakhs = Rs.1.28 crores
which of the following numbers will replace the Question mark?
At an Electronic Data Processing Unit, five out of the eight program sets P, Q, R, S, T, U, V and W are to be operated daily. On any one day except for the first day of a month, only three of the program sets must be the ones that were operated on the previous day.
The program operating must also satisfy the following conditions:
I. If program P is to be operated on a day, V cannot be operated on that day.
II. If Q is to be operated on a day, T must be one of the programs to be operated after Q.
III. If R is to be operated on a day, V must be one of the programs to be operated after R.
IV. The last program to be operated on any day must be either S or U.
Q. Which of the following could be the set of programs to be operated on the first day of a month?
At an Electronic Data Processing Unit, five out of the eight program sets P, Q, R, S, T, U, V and W are to be operated daily. On any one day except for the first day of a month, only three of the program sets must be the ones that were operated on the previous day.
The program operating must also satisfy the following conditions:
I. If program P is to be operated on a day, V cannot be operated on that day.
II. If Q is to be operated on a day, T must be one of the programs to be operated after Q.
III. If R is to be operated on a day, V must be one of the programs to be operated after R.
IV. The last program to be operated on any day must be either S or U.
Q. Which of the following is true of any day's valid program set operation?
If R is operated at fourth place, V must be operated at fifth place (conditional) (iii).
This violates condition (iv)
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