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A 70 cm long wire is to be cut into two pieces so that one piece will be 52тАЛ of the other. How many centimetres will the shorter piece be?
10 cm
25 cm
30 cm
20 cm
20 cm
Sum the ratio parts (2 + 5 = 7). Divide the total length by the sum (70 / 7 = 10). The shorter piece is 2 parts, so 2 * 10 = 20 cm.
Total length of wire = 70 cm, Ratio of two pieces = 2:5
x=SumofRatiosRatiopartтАЛтАЛ├ЧTotalLength
Sum the ratio parts (2 + 5 = 7). Divide the total length by the sum (70 / 7 = 10). The shorter piece is 2 parts, so 2 * 10 = 20 cm.
Mistaking the 'shorter piece' for the ratio part '2' without applying it to the total, or incorrectly identifying 5 as the shorter piece.
Define the ratio
Let the two pieces be in the ratio 2:5. We can express their lengths as 2x and 5x.
2x+5x=70
Calculate the common variable x
Summing the parts gives 7x=70. Solving for x by dividing both sides by 7.
x=770тАЛ=10
Determine the length of the shorter piece
The shorter piece corresponds to the smaller ratio part, which is 2x. Substituting x=10 into the expression.
2├Ч10=20cm
D is correct because the ratio parts are 2 and 5, leading to a calculation of 20cm for the shorter piece.
This concept of partitioning quantities in a given ratio is fundamental in mixtures and alligation, as well as time-speed-distance problems.
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