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11. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

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Solution:
LetthenumberbexandyThen,xy=9375andxy=15xy(x/y)=937515⇒y2=625⇒y=25⇒x=15y=(15×25)=375∴Sumofthenumber=x+y=375+25=400
12. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

Discuss
Solution:
Let the numbers be x and y
Then, xy = 120 and x2 + y2 = 289
∴ (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
∴ x + y = 529  = 23
13. A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

Discuss
Solution:
Let the middle digit be x
Then, 2x = 10 or x = 5. So, the number is either 253 or 352
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253
14. The sum of two number is 25 and their difference is 13. Find their product.

Discuss
Solution:
Let the numbers be x and y
Then, x + y = 25 and x - y = 13
4xy = (x + y)2 - (x- y)2
   = (25)2 - (13)2
   = (625 - 169)
   = 456
∴ xy = 114
15. What is the sum of two consecutive even numbers, the difference of whose squares is 84?

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Solution:
Let the numbers be x and x + 2.
Then, (x + 2)2 - x2 = 84
⇒ 4x + 4 = 84
⇒ 4x = 80
⇒ x = 20.
∴ The required sum
= x + (x + 2)
= 2x + 2
= 42
16. The sum of twice a number and three times of 42 is 238. What is the sum of thrice the number and two times of 42 ?

Discuss
Solution:
Let the number be x
Then,
⇔2x+3×42=238⇔2x+126=238⇔2x=112⇔x=56
∴ Required sum :
=3x+2×42=3×56+2×42=168+84=252
17. By how much is 34th of 568 lesser than 78th of 1008 ?

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Solution:
=78 of 1008−34 of 568=(1008×78)−(568×34)=882−426=456
18. Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is :

Discuss
Solution:
Let the number be x
Then,
⇔3x2−4x=x+50⇔3x2−5x−50=0⇔(3x+10)(x−5)=0⇔x=5
19. What is the greater of the two numbers whose product is 1092 and the sum of the two numbers exceeds their difference by 42 ?

Discuss
Solution:
Let the numbers be x and y
Then,
xy=1092.....(i)
And,
⇔(x+y)−(x−y)=42⇔2y=42⇔y=21
Putting y = 21 in (i), we get :
x=109221=52
Hence, greater number = 52
20. The product of three consecutive even numbers when divided by 8 is 720. The product of their square roots is :

Discuss
Solution:
Let the numbers be x, x + 2 and x + 4
Then,
⇔x(x+2)(x+4)8=720⇔x(x+2)(x+4)=5760∴x×(x+2)×(x+4)=x(x+2)(x+4)=5760=2410

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