Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum.

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Question
Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?
Options
A. 23
B. 24
C. 25
D. 26

Correct Answer

26

Explanation

Let, Hema attempted 'k' sum correctly, then

k x 3 -2 x(35-k) = 60
5k = 130
k = 26

so 26 correct sums.

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Simplification problems

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1. If 3x-y=27 , 3x+y=243 then find the x value
Options
A. 2
B. 8
C. 4
D. 1

Discuss

Correct Answer: 4

Explanation:

Given that $3^{x - y} = 27$ , $3^{x + y} = 243$

$? 3^{x - y} = 3^{3}, 3^{x + y} = 3^{5}$

=> x-y=3, x+y=5

=> x = 4

2. If a+b=5 and 3a+2b=20,then (3a+b)will be :
Options
A. 20
B. 15
C. 25
D. 30

Discuss

Correct Answer: 25

Explanation:

a+b=5 ...(1) and 3a+2b=20 ...(2)

Multiplying (1) by 2 and subtracting from (2), we get : a=10.

Putting a=10 in (1), we get : b=-5

Therefore, (3a+b) = 3 x 10+(-5)=30-5=25.

3. Simplify 413 + 215 + 414 = ?
Options
A. 10 47/60
B. 11 45/73
C. 11 47/36
D. 10 35/48

Discuss

Correct Answer: 10 47/60

Explanation:

The given equation is in Mixed fraction.

Now to solve this type of fractions,

$4 \frac{1}{3} + 2 \frac{1}{5} + 4 \frac{1}{4} = ? ? = (4 + 2 + 4) + (\frac{1}{3} + \frac{1}{5} + \frac{1}{4}) ? = 10 + \frac{47}{60} ? = 10 \frac{47}{60}$

4. 1397 x 1397 = ? Here what replaces '?'
Options
A. 1951609
B. 1821504
C. 2031489
D. 1847879

Discuss

Correct Answer: 1951609

5. 1747 + 13212 - ? = 1123
Options
A. 16
B. 17
C. 18
D. 19

Discuss

Correct Answer: 19

Explanation:

$17 \frac{4}{7} + 13 \frac{2}{12} - ? = 11 \frac{2}{3}$

$\frac{123}{7} + \frac{158}{12} - ? = \frac{35}{3}$

=> $? = \frac{123}{7} + \frac{158}{12} - \frac{35}{3}$

=> ? = $\frac{1476 + 1106 - 980}{84}$

=> ? = 19.07

6. 217 x 217 + 183 x 183 = ?
Options
A. 84521
B. 87487
C. 80578
D. 78458

Discuss

Correct Answer: 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.

7. 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 ?
Options
A. 15
B. 20
C. 10
D. 8

Discuss

Correct Answer: 10

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 => $- 150 + x^{2} + 5 x$

multiplying both sides by -1/10x

=> $x^{2} + 15 x - 10 x - 150 = 0$

=> x(x + 15) - 10(x + 15) = 0

=> x = 10 or -15

As x>0, x = 10.

8. Solve this inequality 3b - 7 < 32?
Options
A. b = 13
B. b < 13
C. b > = 13
D. b < = 13

Discuss

Correct Answer: b < 13

Explanation:

The given 3b - 7 < 32 can be solved as

3b - 7 < 32

3b < 39

b < 13.

9. Simplify and find '?' 48?+32? = 320
Options
A. 4
B. 8
C. 16
D. 32

Discuss

Correct Answer: 16

Explanation:

given

$48 \sqrt{?} + 32 \sqrt{?} = 320$

=> $6 \sqrt{?} + 4 \sqrt{?} = 40$

Now squaring on both sides

=> $36 x ? + 16 x ? + 48 x ? = 1600$

=> 100 x ? = 1600

=> ? = 16

10. Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to ___ ?
Options
A. 3.7
B. 2.7
C. 3.6
D. 2.9

Discuss

Correct Answer: 2.9

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Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?

Simplification problems

Search Results

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