5
Q:

# In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

 A) 160 B) 175 C) 180 D) 195

Explanation:

Suppose the man works overtime for x hours.

Now, working hours in 4 weeks = (5 x 8 x 4) = 160.

${\color{Blue}&space;\therefore&space;}$ 160 x 2.40 + x x 3.20 = 432

=> 3.20x = 432 - 384 = 48

=> x = 15.

Hence, total hours of work = (160 + 15) = 175.

Q:

A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook ?

 A) 15 B) 20 C) 10 D) 8

Explanation:

Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => $\inline \fn_jvn \small -150+x^{2}+5x=0$
multiplying both sides by -1/10x
=> $\inline \fn_jvn \small x^{2}+15x-10x-150=0$
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.

1 1
Q:

A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can he make out of half of the cloth he has ?

 A) 300 B) 150 C) 175 D) 200

Explanation:

Half of the cloth = 37.5/2
From 1 meter he will make 8 pieces
=> in 37.5/2 ---- ?

37.5/2 x 8

= 150.

1 10
Q:

Identify the greatest numbers :

A.   $\fn_jvn 4^{50}$     B.    $\fn_jvn 2^{100}$    C.   $\fn_jvn 16^{25}$

 A) A B) C C) Both A and B D) All are equal

Explanation:

$\fn_jvn 4^{50}$   =   $\fn_jvn \small (2^{2})^{50}$   =   $\fn_jvn \small 2^{100}$   =>  $\fn_jvn 16^{25}$ =   $\fn_jvn \small (2^{4})^{25}$  =   $\fn_jvn \small 2^{100}$

Hence,  $\fn_jvn 4^{50}$ , $\fn_jvn \small 2^{100}$  and $\fn_jvn 16^{25}$ are all equal.

1 10
Q:

217 x 217 + 183 x 183 = ?

 A) 84521 B) 87487 C) 80578 D) 78458

Explanation:

$\inline \fn_jvn \small (217)^{2}+(183)^{2}=(200+17)^{2}+(200-17)^{2}$

= $\inline \fn_jvn \small 2[(200)^{2}+(17)^{2}]$ = 2(40000 + 289) = 80578.

1 26
Q:

Twenty times a positive integer is less than its square by 96. What is the integer ?

 A) 42 B) 36 C) 48 D) 24

Explanation:

Let the integer be x. Then,

x2 - 20x = 96

(x + 4)(x - 24) = 0

x = 24