24
Q:

# Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?

 A) 32 years, 23 years B) 32 years, 29 years C) 35 years, 29 years D) 35 years, 33 years

Answer:   A) 32 years, 23 years

Explanation:

When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.

Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.

Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.

Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.

Q:

In a certain office, $\inline \frac{1}{3}$ of workers are women, $\inline \frac{1}{2}$of the women are married and $\inline \frac{1}{3}$ of the married women have children. If $\inline \frac{3}{4}$ of the men are married and $\inline \frac{2}{3}$ of the married men have children, what part of the workers are without children ?

 A) 5/18 B) 4/9 C) 11/18 D) 17/36

Explanation:

Let the total number of workers be x. Then,

Number of women = $\inline \frac{x}{3}$ and number of men = $\inline \left ( x-\frac{x}{3} \right )$ = $\inline \frac{2x}{3}$

Number of women having children = $\inline \fn_jvn \frac{1}{3}\;of\; \frac{1}{2}\; of\; \frac{x}{3}=\frac{x}{18}$

Number of men having children = $\inline \fn_jvn \frac{2}{3}\;of\; \frac{3}{4}\; of\; \frac{2x}{3}=\frac{x}{3}$

Number of workers having children = $\inline \fn_jvn \left ( \frac{x}{18}+\frac{x}{3} \right )=\frac{7x}{18}$

$\inline \fn_jvn \therefore$ workers having no children = $\inline \fn_jvn \left ( x-\frac{7x}{18} \right )=\frac{11x}{18}=\frac{11}{18}$ of all workers

14 227
Q:

The following question is based on the given data for an examination.

A. Candidates appeared                 10500

B. Passed in all the five subjects     5685

C. Passed in three subjects only     1498

D. Passed in two subjects only       1250

E. Passed in one subject only           835

F. Failed in English only                       78

G. Failed in Maths only                      275

H. Failed in Physics only                    149

I. Failed in Chemistry only                147

J. Failed in Biology only                     221

How many candidates passed in at least four subjects ?

 A) 6555 B) 5685 C) 1705 D) 870

Explanation:

Candidates passed in atleast four subjects

= (Candidates passed in 4 subjects) + (Candidates Passed in all 5 subjects)

= (Candidates failed in only 1 subject ) + ( Candidates passed in all subjects)

= (78 + 275 + 149 + 147 + 221) + 5685 = 870 + 5685 = 6555

8 697
Q:

A man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack?

 A) 106 B) 301 C) 309 D) 400

Explanation:

Clearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (L.C.M of 3, 4, 5, 6) x + 1 i.e., (60x + 1 ) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So the number is 301.

16 545
Q:

Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?

 A) 23 years B) 25 years C) 33 years D) 35 years

Explanation:

Ayush's present age = 10 years.

His mother's present age = (10 + 20) years = 30 years.

Ayush's father's present age = (30 + 5) years = 35 years.

Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.

Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.

69 2034
Q:

In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?

 A) 18 B) 36 C) 45 D) None of these

Explanation:

Let R, G and B represent the number of balls in red, green and blue boxes respectively.

Then,

R + G + B = 108 ...(i),

G + R = 2B ...(ii)

B = 2R ...(iii)

From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.

Putting G = 3R and B = 2R in (i), we get:

R + 3R + 2R = 108 ${\color{Blue}&space;\Rightarrow&space;}$ 6R = 108 ${\color{Blue}&space;\Rightarrow&space;}$ R = 18.

Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.