4
Q:

# The average of 26,29,n,35 and 43 lies between 25 and 35. If n is always an integer and greater than the average  of the given integers then the value of n is :

 A) 33 B) 34 C) 33 D) None of these

Explanation:

Average of 26,29,35 and 43 is 33.25 . Also the average of 26 , 29, n, 35 and 43 lies between 25 and 35 i.e,

$\inline&space;25<\frac{26+29+n+35+43}{5}<35$

$\inline&space;\Rightarrow$ 125 < 26+29+n+35+43 < 175

$\inline&space;\Rightarrow$ 125 < 133 + n < 175

$\inline&space;\Rightarrow$  n < 42

Since the value of n is an integer and greater than 33.25 then 33 < n < 42 for every integer n.

Q:

In a mixture of three varities of oils , the ratio of their weight is 4 : 5 : 8. If 5 kg of oils of the first variety, 10 kg of the second variety and some quantity of oils of the third variety are added to the mixture, the ratio of the weights of three varieties of oils becomes as 5 : 7 : 9 in the final mixture, find the quantity of third variety of oil was ?

 A) 15 kg B) 25 kg C) 35 kg D) 45 kg

Explanation:

Let the ratio of initial quantity of oils be 'x' => 4x, 5x & 8x.
Let k be the quantity of third variety of oil in the final mixture.
Let the ratio of initial quantity of oils be 'y'
From given details,
4x + 5 = 5y ..... (1)
5x + 10 = 7y .....(2)
8x + k = 9y ......(3)

By solving (1) & (2), we get
x = 5 & y = 5

From (3) => k = 5

Therefore, quantity of third variety of oil was 9y = 9(5) = 45kg.

4 89
Q:

The average of marks in 3 subjects is 224. The first subject marks is twice the second and the second subject marks is twice the third. Find the second subject marks ?

 A) 384 B) 96 C) 192 D) 206

Explanation:

Let the third subject marks be 'x'
=> Second subject marks = 2x
=> Third subject marks = 4x
Given avg = 224
x + 2x + 4x = 224 x 3
=> 7x = 224 x 3
=> x = 96
Hence, Second subject marks = 2x = 2 x 96 = 192.

6 110
Q:

It costs Rs. p each to send the first thousand messsages and Rs. q to send each subsequent one . If r is greater than 1,000, how many Rupees will it cost to send r messages ?

 A) 1000 (r - p) + pq B) 1000 p + qr C) 1000 (r - q) + pr D) 1000(p - q) + qr

Explanation:

We need to find the total cost to send r messsages, r > 1000.

The first 1000 messsages will cost Rs.p each (Or)

The total cost of first 1000 messsages = Rs.1000p

The remaining (r - 1000) messsages will cost Rs.q each (Or)

The cost of the (r - 1000) = Rs.(r - 1000)y

Therefore, total cost = 1000p + rq - 1000q

= 1000(p - q) + qr

9 262
Q:

Sriram was conducting an experiment in which the average of 11 observations came to be 92, while the average of first five observations was 89, and that of the last five was 86. What was the measure of the 6th observation ?

 A) 134 B) 137 C) 139 D) 141

Explanation:
This can be done as,

(11 × 92)  -  (5 × 89)  -  (5 × 86)

= 1012- 445 - 430 = 137

8 278
Q:

In a mens hostel, there were 95 students. To accommodate 30 more students the average is decreased by rupees 5. But total expenditure increased by Rs.500. Find the total expenditure of the hostel now ?

 A) Rs. 4680 B) Rs. 4420 C) Rs. 4960 D) Rs. 5480

Explanation:

Let the expenditure on the 95 students be 'x'

Then,

95x + 500 = 120(x – 5)
95x + 500 = 120x - 600
120x - 95x = 1100
25x = 1100
=> x = 44

Therefore, total expenditure of the hostel becomes
95 x 44 + 500 = 4680.