In a quality check of a company, the number of items which passed the test and the number of those w

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04 Oct 2022 Ratio & Proportion

In a quality check of a company, the number of items which passed the test and the number of those which failed were in the ratio 19:4. If later nine more items were tested and the number of failed items were 3 less than earlier, the ratio of items passed to failed was 29:5. The number of items which were initially tested is:

OPtion

1) 170
2) 138
3) 184
4) 161
5) 207
6) 133
7) 154
8) 177
9) 134
10) None of these

Solution

Let the number of items whch passed the test = 19x and number of failed = 4x
∴ Total no. of items tested = 23x
New number of items tested = 23x + 9
New number of failed items = 4x - 3
∴ New number of passed items = (23x + 9) - (4x - 3) = 19x + 12
New ratio of items passed to failed = (19x+12) / (4x-3) = 29/5
95x + 60 = 116x - 87
21x = 147
x = 7
.'. Items tested initially = 23*7 = 161

Correct Option: 4 Best Solution (2)

G.S.Kantharao   1 year AGO

Let the initial tested pass,fail=19x,4x
Given 19x+12:4x-3=29:5
Product of extremes=Product of means
5(19x+12)=29(4x-3)
95x+60=116x-87
21x=147=>x=7
Total no of tested items are 23x=23*7=161
My option is 4👈

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RAMADURAI NATESAN   1 year AGO

Let N be no.of items. P = 19N/23.F=4N/23. 5(N+9)/34=(4N/23) - 3. Solving N = 161

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