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Question

# If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as the remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the sum of the numbers

A
34
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B
43
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C
47
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D
74
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Solution

## The correct option is B 43Let the larger number be x and the smaller one be y. We use the division statement that Dividend =(Divisor x Quotient) + RemainderSo, in the first case,3x=4y+3⇒4y=3x−3 ...........(i) And 7y=5x+1 .............(ii).Multiplying (i) by 7 & (ii) by 4, we get28y=21x−21 ......(iii) and28y=20x+4 .....(iv).Subtracting eq (iv) from (iii) we get, x−25=0⇒x=25⇒4y=3×25−3=72∴y=724=18⇒x+y=25+18=43

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