Xavier Aptitude Test 2013 Paper

Question : 58 of 121

Marks: +1, -0

Mr. Mehra is planning for higher education expenses of his two sons aged 15 and 12. He plans to divide Rs 15 lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs. 21 lakhs each when they reach the age of 21. He is looking for plan that will give him a simple interest per annum. The rates of interest of the plans for his younger son and elder son should be

5% and 7.5% respectively
8% and 12% respectively
10% and 15% respectively
15% and 22.5% respectively
20% and 30% respectively

Validate

Solution:

(e) For the younger child Rs. 7.5 lakh should become 21 lakhs in 9 years.
Hence,
Amount = Principal + Simple Interest

21=\ {P}+ {\ {P} \× \ {R}_{1} ×{T}}/{100}

21=7.5 [1+\ (\ {\ {R}_{1}}/{100} )^{9} ]

21 \× 100=7.5 \×100+7.5 \t×{R}_{1} \× 9

7.5 ×{R}_{1} × 9=(21-7.5) 100

\ {R}_{1}= {13.5 \× 100}/{7.5 \× 9}=20 \%

Similarly, for the elder son, Rs. 7.5 lakh should become in 6 years.
Hence, Amount = Principal + Simple Interest

21=7.5 [1+\ ( {\ {R}_{2}}/{100}\ )^{6}\ ]

21 \× 100=7.5 \×100+7.5 \×{R}_{2} \× 6

7.5 ×{R}_{2} × 6=(21-7.5) ×100

\ {R}_{2}=\ {13.5 × 100}/{7.5 \× 6}=30 \%

Hence, the correct answer is option (e).

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