1499+ Simplification Questions and Answers With Explanation

Q:

If a + b + c = 13, $a^{2} + b^{2} + c^{2} = 69$ then find the ab + bc + ca :

A) 10	B) 30
C) 50	D) 70

Answer & Explanation Answer: C) 50

Explanation:

${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$

$2 (a b + b c + c a) = {(a + b + c)}^{2} - (a^{2} + b^{2} + c^{2}) = 169 - 69 = 100 = (a b + b c + c a) = 50$

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52 30304

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

Answer & Explanation Answer: B) 175

Explanation:

Suppose the man works overtime for x hours.

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

Therefore, 160 * 2.40 + x * 3.20 = 432

=> 3.20x = 432 - 384 = 48

=> x = 15.

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

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34 30148

Q:

A tank is 2/5 full. If 16 litres of water is added to the tank, it becomes 6/7 full. The capacity of the tank is:

A) 28 litres	B) 32 litres
C) 35 litres	D) 42 litres

Answer & Explanation Answer: C) 35 litres

Explanation:

Let the capacity of the tank be x litres.

Then, (6x/7 - 2x/5) = 16 <=> 30x - 14x = 16*35 <=> x = 35

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34 22714

Q:

The total of 324 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is :

A) 50	B) 100
C) 150	D) 200

Answer & Explanation Answer: D) 200

Explanation:

Let the number of 20 paise coins be x. Then the no of 25 paise coins = (324 - x).

0.20 * (x) + 0.25 (324 - x) = 71 => x = 200..

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19 16650

Q:

The difference of $\frac{1}{8}$ and its reciprocal is equal to :

A) 1/8	B) 4/3
C) 15/16	D) 105/304

Answer & Explanation Answer: D) 105/304

Explanation:

Required difference = 19/16 - 16/19 = 105/304..

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42 15477

Q:

217 x 217 + 183 x 183 = ?

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

Answer & Explanation Answer: C) 80578

Explanation:

${(217)}^{2} + {(183)}^{2}$

= ${(200 + 17)}^{2} + {(200 - 17)}^{2}$

It is in the form of ${(a + b)}^{2} + {(a - b)}^{2} = 2 (a^{2} + b^{2})$

= 2(40000 + 289) = 80578.

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20 14786

Q:

In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?

A) 6	B) 10
C) 8	D) 12

Answer & Explanation Answer: D) 12

Explanation:

Let the number of buffaoes be x and number of ducks be y.

Then 4x + 2y = 2(x + y) + 24

=> 2x = 24

=> x = 12.

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18 14544

Q:

The highest score in an inning was 3/11 of the total and the next highest was 3/11 of the reminder . If the score differ by 9, the total score was :

A) 110	B) 121
C) 132	D) 143

Answer & Explanation Answer: B) 121

Explanation:

Let the score be x. Then the highest score = 3x/11.

Reminder = (x - 3x/11) = 8x/11 .Next the highest score = 3/11 of 8x/11 = 24x/121.

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