Question

70. A man has Rs. 10,000 to Invest. He invests
Rs. 4000 at 5% and Rs. 3500 at 4%. In order
to have a yearly Income of Rs. 500, he must
invest the remaining Rs. 2500 at what rate of
Interest?
(A) 6%
(B) 6.2%
(C) 6 3%
(D) 6.4%​

Answer 1

Answer:

6.4℅

Step-by-step explanation:

given

• principle = ₹10000
• 1st investment = ₹4000 @ 5℅
• 2nd investment = ₹3500 @ 4℅
• total intrest = ₹500
• time = 1 year

now,

we know that

simple intrest = p*r*t/100

so,

intrest gained from 1st investment =>

=> 4000*5*1/100 = ₹200

&

intrest gained from 2nd investment =>

=> 3500*4*1/100 = ₹140

but given that total intrest = ₹500

so,

₹500 - (200+140) = 500 - 340 = ₹160

hence,

intrest on ₹2500 = ₹160

so,

rate of intrest = intrest×100 / principle × time

=> rate = 160 × 100 / 2500 × 1

=> rate = 6.4℅ (answer)

Answer 2

Answer:

Step-by-step explanation:

Solution:

Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.

= $ 4000 × 5/100.

= $ 4000 × 0.05.

= $ 200.

Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.

= $ 3500 × 4/100.

= $ 3500 × 0.04.

= $ 140.

Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.

Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.

= $ 160.

Total invested amount = $ 4000 + $ 3500 = $7500.

Remaining invest amount = $ 10000 - $ 7500 = $ 2500.

We know that, Interest = Principal × Rate × Time

Interest = $ 160,

Principal = $ 2500,

Rate = r [we need to find the value of r],

Time = 1 year.

160 = 2500 × r × 1.

160 = 2500r

160/2500 = 2500r/2500 [divide both sides by 2500]

0.064 = r

r = 0.064

Change it to a percent by moving the decimal to the right two places r = 6.4 %

Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.

Answer: (e)