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1, Amina thinks of a number and subtracts5from it. She multiplies the result by 8. Theresult now obtained is 3 times the same number she thought of. What is the number?2. A positive number is 5 times another number. If 21 is added to both the numbers,then one of the new numbers becomes twice the other new number. What are thenumbers?3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it isfound that the resulting new number is greater than the original number by 27. Whatis the two-digit number?4. One of the two digits of a two digit number is three times the other digit li youinterchange the digits of this two-digit number and add the resulting sumber to theoriginal number, you get 88. What is the original number?5. Shobo's mother's present age is six times Shobo's present age. Shobo's age fiveyears from now will be one third of his mother's present age. What are theirpresent ages?. There is a narrow rectangular plot, reserved for a school, in Mahuli village. Thelength and breadth of the plot are in the ratio 11:4. At the rate 100 per metre it willcost the village panchayat 75000 to fence the plot. What are the dimensions ofthe plot?Hasan buys two kinds of cloth materials for school uniforms, shirt material thatcosts him 50 per metre and trouser material that costs him 90 per metre. |
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Answer» Linear Equations Exercise 2.4 Part 1 Question 1: Amina thinks of a number and subtracts 5 2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number? Solution: Let the number thought by Anamika = a According to question ( Number − 5 2 ) × 8 = 3 × Number Or, ( a − 5 2 ) × 8 = 3 × a Or, ( a − 5 2 ) × 8 = 3 a After removing the bracket we get: 8 a − 5 2 × 8 = 3 a Or, 8 a − 40 2 = 3 a Or, 8 a − = 3 a After transposing 3a to LHS we get: 8 a − 20 − 3 a = 0 Or, 8 a − 3 a − 20 = 0 Or, 5 a − 20 = 0 After transposing -20 to RHS we get: 5 a = 20 After dividing both sides by 5 we get: 5 a 5 = 20 5 Or, a = 4 Thus, the required number = 4 Answer Question 2: A positive number is 5 times another number. If 21 is added to both the numbers,then one of the new numbers becomes twice the other new number. What are the numbers? Solution: Let the GIVEN positive number = a Therefore, another number which is 5 times of it = 5a Now, after adding 21 to both of the number, First number = a + 21 Second number = 5 a + 21 According to question, one new number becomes twice of the other new number Therefore, Second number = 2 x first number i.e. 5 a + 21 = 2 ( a + 21 ) ⇒ 5 a + 21 = 2 a + 42 By transposing ‘2A’ to LHS, we get ⇒ 5a + 21 – 2a = 42 Now, after transposing 21 to RHS, we get ⇒ 5 a – 2 a = 42 – 21 ⇒ 3 a = 21 After dividing both sides by 3, we get 3 a 3 = 21 3 Or, a = 7 Therefore, another number 5 a = 5 × 7 = 35 Thus, required numbers are 7 and 35 Answer Question 3: Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number? Solution: Let the number at ones place of two digit number = a According to question, the sum of digits of given two digit number = 9 i.e. Digit at tens place + digit at ones place = 9 Or, Digit at tens place + a = 9 By transposing ‘a’ to RHS, we get Digit at tens place = 9 – a Thus, the number = 10 ( 9 – a ) + a After interchange of digit, the number = 10 a + ( 9 – a ) Since, number obtained after interchange of digit is greater than the original number by 27 Therefore, New number – 27 = Original number Here, we have original number = 10 ( 9 – a ) + a And, new number = 10 a + ( 9 – a ) ⇒ 10 a + ( 9 – a ) – 27 = 10 ( 9 – a ) + a ⇒ 10 a + 9 – a – 27 = 90 – 10 a + a ⇒ 10 a – a + 9 – 27 = 90 – 9 a ⇒ 9 a – 18 = 90 – 9 a
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