Question

1). A man has 40 belts and handkerchiefs in number. If he had 5 more handkerchiefs and 5 less belts, the number of handkerchiefs becomes four times the number of belts. Find the original number of each

Answer 1

Let the no of handkerchief be x and the no. of belts be y.
x+y=40......(i)
now from the II condition,
(x+5)+(y-5)=40
and (x+5)=4(y-5)
x+5=4y-20
x-4y=-25(ii)
now subtract eqn (ii) from(i) we get,
5y=65
y=13 and x=27 ,these are the original no.s of belts and handkerchiefs.
now if we have 5 more handkerchiefs(x) i.e x=32
and 5 less belts i.e. y=8
we can see no. of handkerchiefs are four times the no. of belts.

Answer 2

the no of handkerchief be x and the no. of belts be y.

x+y=40......(i)

now from the II condition,

(x+5)+(y-5)=40

and (x+5)=4(y-5)

x+5=4y-20

x-4y=-25(ii)

now subtract eqn (ii) from(i) we get,

5y=65

y=13 and x=27 ,these are the original no.s of belts and handkerchiefs.

now if we have 5 more handkerchiefs(x) i.e x=32

and 5 less belts i.e. y=8

we can see no. of handkerchiefs are four times the no. of belts

x=32,y=8

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