Number System
-  The product of two positive numbers is 2500. If one number is four times the other, then the sum of the two numbers is :
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                        View Hint View Answer Discuss in Forum Let one of the positive numbers be x. 
 ∴ The other will be 4x
 Now, 4x × x = 2500
 ⇒ x2 = 2500 ÷ 4 = 625
 ∴ x = 625 = 25
 ∴ Sum of the two numbers
 = 5x = 5 × 25 =125Correct Option: BLet one of the positive numbers be x. 
 ∴ The other will be 4x
 Now, 4x × x = 2500
 ⇒ x2 = 2500 ÷ 4 = 625
 ∴ x = 625 = 25
 ∴ Sum of the two numbers
 = 5x = 5 × 25 =125
-  380 mangoes are distributed among some boys and girls who are 85 in number. Each boy gets four mangoes and each girl gets five. The number of boys is
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                        View Hint View Answer Discuss in Forum Let number of boys = x 
 and number of girls = 85 – x
 According to the question,
 x × 4 + (85 – x ) × 5 = 380
 ⇒ 4x + 425 – 5x = 380
 ⇒ x = 45Correct Option: DLet number of boys = x 
 and number of girls = 85 – x
 According to the question,
 x × 4 + (85 – x ) × 5 = 380
 ⇒ 4x + 425 – 5x = 380
 ⇒ x = 45
-   99 1 + 99 2 + 99 3 + 99 4 + 99 5 + 99 6  7 7 7 7 7 7 
 is equal to
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                        View Hint View Answer Discuss in Forum Expression =  99 + 1 + 99 + 2 + 99 + 3 + .......+ 99 + 6  7 7 7 7 = (99 ×6) +  1 + 2 + 3 + 4 + 5 + 6  7 7 7 7 7 7 = 594 +  1 + 2 + 3 + 4 + 5 + 6  7 = 594 + 21 = 594 + 3 = 597 7 
 Correct Option: DExpression =  99 + 1 + 99 + 2 + 99 + 3 + .......+ 99 + 6  7 7 7 7 = (99 ×6) +  1 + 2 + 3 + 4 + 5 + 6  7 7 7 7 7 7 = 594 +  1 + 2 + 3 + 4 + 5 + 6  7 = 594 + 21 = 594 + 3 = 597 7 
 
-  The sum and product of two numbers are 10 and 24 respectively. The sum of their reciprocals is
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                        View Hint View Answer Discuss in Forum Let the numbers be x and y. 
 ∴ x + y = 10 and xy = 24∴ x + y = 1 + 1 = 10 = 5 xy y x 24 12 Correct Option: BLet the numbers be x and y. 
 ∴ x + y = 10 and xy = 24∴ x + y = 1 + 1 = 10 = 5 xy y x 24 12 
-  The product of two numbers is 120. The sum of their squares is 289. The difference of these two numbers is
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                        View Hint View Answer Discuss in Forum Let the numbers be x and y. 
 xy = 120
 x2 + y2 = 289
 (x − y)2 = x2 + y2 − 2xy
 = 289 – 2× 120 = 289 – 240 = 49
 ∴ x – y = 7Correct Option: BLet the numbers be x and y. 
 xy = 120
 x2 + y2 = 289
 (x − y)2 = x2 + y2 − 2xy
 = 289 – 2× 120 = 289 – 240 = 49
 ∴ x – y = 7
 
	